% Structured bibliography for Urysohnspace.tex
% DOI values were included only when the work and edition were verified.

@unpublished{AIb,
  author = {Asuman G\"{u}ven Aksoy and Zair Ibragimov},
  title = {Finite ball intersection property of the {Urysohn} universal space},
  year = {2013},
  eprint = {1309.7381},
  status = {Preprint}
}

@article{Ant,
  author = {Sergey A. Antonyan},
  title = {The {Gromov--{Hausdorff}} hyperspace of a Euclidean space},
  journal = {Advances in Mathematics},
  volume = {363},
  pages = {106977},
  year = {2020},
  doi = {10.1016/j.aim.2020.106977}
}

@article{BLMS,
  author = {Florent Baudier and Gilles Lancien and Pavlos Motakis and Thomas Schlumprecht},
  title = {Coarse and Lipschitz universality},
  journal = {Fundamenta Mathematicae},
  volume = {254},
  number = {2},
  pages = {181--214},
  year = {2021},
  doi = {10.4064/fm956-9-2020},
  eprint = {2004.04806}
}

@article{Be,
  author = {V. N. Berestovskii},
  title = {On {Urysohn}'s $\mathbb{R}$-tree},
  journal = {Siberian Mathematical Journal},
  volume = {60},
  number = {1},
  pages = {10--19},
  year = {2019},
  doi = {10.1134/S0037446619010026}
}

@article{BDKP,
  author = {V. Bilet and O. Dovgoshey and M. K\"{u}\c{c}\"{u}kaslan and E. Petrov},
  title = {Minimal universal metric spaces},
  journal = {Annales Academiae Scientiarum Fennicae Mathematica},
  volume = {42},
  pages = {1019--1064},
  year = {2017},
  doi = {10.5186/aasfm.2017.4261}
}

@article{Bielas,
  author = {Wojciech Bielas},
  title = {An example of a rigid $\kappa$-superuniversal metric space},
  journal = {Topology and its Applications},
  volume = {208},
  pages = {127--142},
  year = {2016},
  doi = {10.1016/j.topol.2016.05.010}
}

@article{Bogatyi,
  author = {S. A. Bogatyi},
  title = {Compact homogeneity of {Urysohn}'s universal metric space},
  journal = {Russian Mathematical Surveys},
  volume = {55},
  number = {2},
  pages = {332--333},
  year = {2000},
  doi = {10.1070/RM2000v055n02ABEH000273}
}

@incollection{CameronRandomGraph,
  author = {Peter J. Cameron},
  title = {The random graph},
  booktitle = {The Mathematics of Paul Erd{\H{o}}s II},
  edition = {2},
  publisher = {Springer},
  address = {New York},
  pages = {353--378},
  year = {2013},
  doi = {10.1007/978-1-4614-7254-4_22},
  eprint = {1301.7544}
}

@unpublished{BrazasArc,
  author = {Jeremy Brazas},
  title = {Constructing arcs from paths using {Zorn}'s lemma},
  year = {2022},
  eprint = {2207.07242},
  status = {Preprint}
}

@article{Bo2002,
  author = {S. A. Bogatyi},
  title = {Metrically homogeneous spaces},
  journal = {Russian Mathematical Surveys},
  volume = {57},
  number = {2},
  pages = {221--240},
  year = {2002},
  doi = {10.1070/RM2002v057n02ABEH000495}
}

@article{BLPS,
  author = {Anthony Bonato and Claude Laflamme and Michael Pawliuk and Norbert Sauer},
  title = {Distinguishing number of universal homogeneous {Urysohn} metric spaces},
  journal = {The Electronic Journal of Combinatorics},
  volume = {29},
  number = {3},
  pages = {P3.58},
  year = {2022},
  doi = {10.37236/8370},
  eprint = {1811.06023}
}

@book{Bourbaki,
  author = {Nicolas Bourbaki},
  title = {General Topology: Chapters 1--4},
  publisher = {Springer-Verlag},
  address = {Berlin},
  year = {1989},
  isbn = {978-0-387-19374-8}
}

@book{BourbakiV,
  author = {Nicolas Bourbaki},
  title = {General Topology: Chapters 5--10},
  publisher = {Springer-Verlag},
  address = {Berlin and Heidelberg},
  edition = {1},
  year = {1989},
  isbn = {978-3-540-64563-4}
}

@article{BNT,
  author = {David Bryant and Andr\'{e} Nies and Paul Tupper},
  title = {A universal separable diversity},
  journal = {Analysis and Geometry in Metric Spaces},
  volume = {5},
  pages = {138--151},
  year = {2017},
  doi = {10.1515/agms-2017-0008}
}

@article{CV,
  author = {Peter J. Cameron and Anatoly M. Vershik},
  title = {Some isometry groups of the {Urysohn} space},
  journal = {Annals of Pure and Applied Logic},
  volume = {143},
  number = {1--3},
  pages = {70--78},
  year = {2006},
  doi = {10.1016/j.apal.2005.08.001}
}

@article{CT,
  author = {Gabriel Conant and Caroline Terry},
  title = {Model theoretic properties of the {Urysohn} sphere},
  journal = {Annals of Pure and Applied Logic},
  volume = {167},
  number = {1},
  pages = {49--72},
  year = {2016},
  doi = {10.1016/j.apal.2015.09.003}
}

@phdthesis{conantthesis,
  author = {Gabriel Conant},
  title = {Model Theory and Combinatorics of Homogeneous Metric Spaces},
  school = {University of Illinois at Chicago},
  year = {2015}
}

@article{conant,
  author = {Gabriel Conant},
  title = {Distance structures for generalized metric spaces},
  journal = {Annals of Pure and Applied Logic},
  volume = {168},
  number = {3},
  pages = {622--650},
  year = {2017},
  doi = {10.1016/j.apal.2016.10.002}
}

@article{conant2,
  author = {Gabriel Conant},
  title = {Neostability in countable homogeneous metric spaces},
  journal = {Annals of Pure and Applied Logic},
  volume = {168},
  number = {6},
  pages = {1442--1471},
  year = {2017},
  doi = {10.1016/j.apal.2017.01.008}
}

@article{CL,
  author = {Samuel Coskey and Martino Lupini},
  title = {A {L\'{o}pez--Escobar} theorem for metric structures, and the topological {Vaught} conjecture},
  journal = {Fundamenta Mathematicae},
  volume = {234},
  number = {1},
  pages = {55--72},
  year = {2016},
  doi = {10.4064/fm135-1-2016},
  eprint = {1405.2859}
}

@article{DLPS,
  author = {Claude Delhomm\'{e} and Claude Laflamme and Maurice Pouzet and Norbert Sauer},
  title = {Divisibility of countable metric spaces},
  journal = {European Journal of Combinatorics},
  volume = {28},
  number = {6},
  pages = {1746--1769},
  year = {2007},
  doi = {10.1016/j.ejc.2006.06.024}
}

@article{Doucha,
  author = {Michal Doucha},
  title = {Non-abelian group structure on the {Urysohn} universal space},
  journal = {Fundamenta Mathematicae},
  volume = {228},
  number = {3},
  pages = {251--263},
  year = {2015},
  doi = {10.4064/fm228-3-3}
}

@article{Doucha2017,
  author = {Michal Doucha},
  title = {Universal and homogeneous structures on the {Urysohn} and {Gurarij} spaces},
  journal = {Israel Journal of Mathematics},
  volume = {218},
  number = {1},
  pages = {299--330},
  year = {2017},
  doi = {10.1007/s11856-017-1466-2}
}

@article{Doucha17,
  author = {Michal Doucha},
  title = {Metrically universal abelian groups},
  journal = {Transactions of the American Mathematical Society},
  volume = {369},
  number = {3},
  pages = {5981--5998},
  year = {2017},
  doi = {10.1090/tran/7059}
}

@mastersthesis{GreThesis,
  author = {Jan Greb\'{\i}k},
  title = {Between Homogeneity and Rigidity},
  school = {Charles University},
  year = {2016}
}

@article{Gre,
  author = {Jan Greb\'{\i}k},
  title = {A rigid {Urysohn}-like metric space},
  journal = {Proceedings of the American Mathematical Society},
  volume = {145},
  number = {9},
  pages = {4049--4060},
  year = {2017},
  doi = {10.1090/proc/13511}
}

@article{Gre2018,
  author = {Jan Greb\'{\i}k},
  title = {An example of a {Fra\"{\i}ss\'{e}} class without a {Kat\v{e}tov} functor},
  journal = {Applied Categorical Structures},
  volume = {26},
  number = {1},
  pages = {1--6},
  year = {2018},
  doi = {10.1007/s10485-016-9469-4}
}

@book{GK,
  author = {Su Gao and Alexander S. Kechris},
  title = {On the Classification of {Polish} Metric Spaces up to Isometry},
  series = {Memoirs of the American Mathematical Society},
  volume = {161},
  number = {766},
  publisher = {American Mathematical Society},
  address = {Providence, RI},
  year = {2003},
  doi = {10.1090/memo/0766}
}

@article{GS,
  author = {Su Gao and Chuang Shao},
  title = {{Polish} ultrametric {Urysohn} spaces and their isometry groups},
  journal = {Topology and its Applications},
  volume = {158},
  number = {3},
  pages = {492--508},
  year = {2011},
  doi = {10.1016/j.topol.2010.12.003}
}

@book{Greenbook,
  author = {Mikhail Gromov},
  title = {Metric Structures for Riemannian and Non-Riemannian Spaces},
  series = {Progress in Mathematics},
  volume = {152},
  publisher = {Birkh\"{a}user},
  address = {Boston},
  year = {1999},
  isbn = {0-8176-3898-9},
  note = {Based on the 1981 French original; with appendices by M. Katz, P. Pansu, and S. Semmes; translated by Sean Michael Bates}
}

@incollection{Ha,
  author = {Felix Hausdorff},
  title = {Der metrische separable Universalraum},
  booktitle = {Gesammelte Werke, Band III: Mengenlehre, Deskriptive Mengenlehre und Topologie},
  pages = {762--769},
  publisher = {Springer},
  address = {Berlin},
  year = {2008},
  doi = {10.1007/978-3-540-76807-4\_28},
  note = {Original work published in 1924; commentary by H. Herrlich, M. Hu\v{s}ek, and G. Preuss}
}

@article{Hechler,
  author = {Stephen H. Hechler},
  title = {Large superuniversal metric spaces},
  journal = {Israel Journal of Mathematics},
  volume = {14},
  pages = {115--148},
  year = {1973},
  doi = {10.1007/BF02762669}
}

@techreport{Hei,
  author = {Juha Heinonen},
  title = {Geometric Embeddings of Metric Spaces},
  institution = {University of Jyv\"{a}skyl\"{a}},
  year = {2003},
  url = {https://www.math.jyu.fi/research/reports/rep90.pdf}
}

@book{Hodges,
  author = {Wilfrid Hodges},
  title = {Model Theory},
  series = {Encyclopedia of Mathematics and its Applications},
  volume = {42},
  publisher = {Cambridge University Press},
  address = {Cambridge},
  year = {1993},
  doi = {10.1017/CBO9780511551574}
}

@article{Holmes,
  author = {M. R. Holmes},
  title = {The universal separable metric space of {Urysohn} and isometric embeddings thereof in {Banach} spaces},
  journal = {Fundamenta Mathematicae},
  volume = {140},
  number = {3},
  pages = {199--223},
  year = {1992},
  doi = {10.4064/fm-140-3-199-223}
}

@article{Holmes2,
  author = {M. R. Holmes},
  title = {The {Urysohn} space embeds in {Banach} spaces in just one way},
  journal = {Topology and its Applications},
  volume = {155},
  number = {14},
  pages = {1479--1482},
  year = {2008},
  doi = {10.1016/j.topol.2008.03.013}
}

@article{Hub,
  author = {Jan Hubi\v{c}ka and Jaroslav Ne\v{s}et\v{r}il},
  title = {A finite presentation of the rational {Urysohn} space},
  journal = {Topology and its Applications},
  volume = {155},
  number = {14},
  pages = {1483--1492},
  year = {2008},
  doi = {10.1016/j.topol.2007.06.022}
}

@article{huhu,
  author = {G. E. Huhunai\v{s}vili},
  title = {On a property of {Urysohn}'s universal metric space},
  journal = {Doklady Akademii Nauk SSSR},
  volume = {101},
  pages = {607--610},
  year = {1955},
  language = {Russian}
}

@article{Hu,
  author = {Miroslav Hu\v{s}ek},
  title = {{Urysohn} universal space, its development and {Hausdorff}'s approach},
  journal = {Topology and its Applications},
  volume = {155},
  number = {14},
  pages = {1493--1501},
  year = {2008},
  doi = {10.1016/j.topol.2008.03.020}
}

@article{J,
  author = {Charles Joiner},
  title = {On {Urysohn}'s universal separable metric space},
  journal = {Fundamenta Mathematicae},
  volume = {73},
  number = {1},
  pages = {51--58},
  year = {1971},
  doi = {10.4064/fm-73-1-51-58}
}

@unpublished{KT,
  author = {Zakhar Kabluchko and Katrin Tent},
  title = {Universal-homogeneous structures are generic},
  year = {2017},
  doi = {10.48550/arXiv.1710.06137},
  eprint = {1710.06137}
}

@inproceedings{Ka,
  author = {Miroslav Kat\v{e}tov},
  title = {On universal metric spaces},
  booktitle = {General Topology and its Relations to Modern Analysis and Algebra VI},
  series = {Research and Exposition in Mathematics},
  volume = {16},
  pages = {323--330},
  publisher = {Heldermann},
  address = {Berlin},
  year = {1988},
  note = {Proceedings of the Sixth Prague Topological Symposium, Prague, 1986}
}

@article{Kubis2010,
  author = {Wies{\l}aw Kubi\'{s} and Matatyahu Rubin},
  title = {Extension and reconstruction theorems for the {Urysohn} universal metric space},
  journal = {Czechoslovak Mathematical Journal},
  volume = {60},
  number = {1},
  pages = {1--29},
  year = {2010},
  doi = {10.1007/s10587-010-0001-y},
  eprint = {math/0504357}
}

@unpublished{KubisNotes,
  author = {Wies{\l}aw Kubi\'{s}},
  title = {Universal Homogeneous Structures},
  year = {2012},
  status = {Lecture notes},
  url = {https://users.math.cas.cz/~kubis/pdfs/FLimits_course_ver1.pdf}
}

@article{KM,
  author = {Wies{\l}aw Kubi\'{s} and Dragan Ma\v{s}ulovi\'{c}},
  title = {{Kat\v{e}tov} functors},
  journal = {Applied Categorical Structures},
  volume = {25},
  number = {4},
  pages = {569--602},
  year = {2017},
  doi = {10.1007/s10485-016-9461-z},
  eprint = {1412.1850}
}

@article{L,
  author = {Davorin Le\v{s}nik},
  title = {Constructive {Urysohn} universal metric space},
  journal = {Journal of Universal Computer Science},
  volume = {15},
  number = {6},
  pages = {1236--1263},
  year = {2009},
  doi = {10.3217/jucs-015-06-1236}
}

@article{LS,
  author = {Lionel Nguyen Van Th\'{e} and Norbert W. Sauer},
  title = {The {Urysohn} sphere is oscillation stable},
  journal = {Geometric and Functional Analysis},
  volume = {19},
  number = {2},
  pages = {536--557},
  year = {2009},
  doi = {10.1007/s00039-009-0007-5}
}

@article{McShane,
  author = {Edward J. McShane},
  title = {Extension of range of functions},
  journal = {Bulletin of the American Mathematical Society},
  volume = {40},
  number = {12},
  pages = {837--842},
  year = {1934},
  doi = {10.1090/S0002-9904-1934-05978-0}
}

@article{Mell2006,
  author = {Julien Melleray},
  title = {Stabilizers of closed sets in the {Urysohn} space},
  journal = {Fundamenta Mathematicae},
  volume = {189},
  number = {1},
  pages = {53--60},
  year = {2006},
  doi = {10.4064/fm189-1-4}
}

@article{Mell2007,
  author = {Julien Melleray},
  title = {On the geometry of {Urysohn}'s universal metric space},
  journal = {Topology and its Applications},
  volume = {154},
  number = {2},
  pages = {384--403},
  year = {2007},
  doi = {10.1016/j.topol.2006.05.005}
}

@article{Mell2008,
  author = {Julien Melleray},
  title = {Some geometric and dynamical properties of the {Urysohn} space},
  journal = {Topology and its Applications},
  volume = {155},
  number = {14},
  pages = {1531--1560},
  year = {2008},
  doi = {10.1016/j.topol.2007.04.029}
}

@article{Mell2016,
  author = {Julien Melleray},
  title = {{Polish} groups and {Baire} category methods},
  journal = {Confluentes Mathematici},
  volume = {8},
  number = {1},
  pages = {89--164},
  year = {2016},
  doi = {10.5802/cml.28}
}

@article{MV,
  author = {Julien Melleray and Fedor V. Petrov and Anatoly M. Vershik},
  title = {Linearly rigid metric spaces and the embedding problem},
  journal = {Fundamenta Mathematicae},
  volume = {199},
  number = {2},
  pages = {177--194},
  year = {2008},
  doi = {10.4064/fm199-2-6}
}

@article{Neumann,
  author = {John von Neumann},
  title = {Ein System algebraisch unabh\"{a}ngiger Zahlen},
  journal = {Mathematische Annalen},
  volume = {99},
  pages = {134--141},
  year = {1928},
  doi = {10.1007/BF01459089}
}

@article{Nie,
  author = {Piotr Niemiec},
  title = {Central subsets of {Urysohn} universal spaces},
  journal = {Commentationes Mathematicae Universitatis Carolinae},
  volume = {50},
  number = {3},
  pages = {445--461},
  year = {2009}
}

@article{Niefun,
  author = {Piotr Niemiec},
  title = {{Urysohn} universal spaces as metric groups of exponent $2$},
  journal = {Fundamenta Mathematicae},
  volume = {204},
  number = {1},
  pages = {1--6},
  year = {2009},
  doi = {10.4064/fm204-1-1}
}

@article{Nie2011,
  author = {Piotr Niemiec},
  title = {Topological structure of {Urysohn} universal spaces},
  journal = {Topology and its Applications},
  volume = {158},
  number = {3},
  pages = {352--359},
  year = {2011},
  doi = {10.1016/j.topol.2010.11.011}
}

@article{Niecat,
  author = {Piotr Niemiec},
  title = {Functor of extension of contractions on {Urysohn} universal spaces},
  journal = {Applied Categorical Structures},
  volume = {19},
  number = {6},
  pages = {959--967},
  year = {2011},
  doi = {10.1007/s10485-009-9218-z}
}

@article{NieANR,
  author = {Piotr Niemiec},
  title = {A note on {ANR}'s},
  journal = {Topology and its Applications},
  volume = {159},
  number = {1},
  pages = {315--321},
  year = {2012},
  doi = {10.1016/j.topol.2011.09.037}
}

@article{Nie2013,
  author = {Piotr Niemiec},
  title = {Universal valued Abelian groups},
  journal = {Advances in Mathematics},
  volume = {235},
  pages = {398--449},
  year = {2013},
  doi = {10.1016/j.aim.2012.12.005}
}

@article{Pestov1,
  author = {Vladimir G. Pestov},
  title = {{Ramsey--Milman} phenomenon, {Urysohn} metric spaces, and extremely amenable groups},
  journal = {Israel Journal of Mathematics},
  volume = {127},
  pages = {317--357},
  year = {2002},
  doi = {10.1007/BF02784537},
  note = {Corrigendum: Israel Journal of Mathematics 145 (2005), 375--379, DOI 10.1007/BF02786701}
}

@book{Pestov2,
  author = {Vladimir Pestov},
  title = {Dynamics of Infinite-Dimensional Groups: The {Ramsey--Dvoretzky--Milman} Phenomenon},
  series = {University Lecture Series},
  volume = {40},
  publisher = {American Mathematical Society},
  address = {Providence, RI},
  year = {2006},
  isbn = {978-0-8218-4137-2},
  doi = {10.1090/ulect/040}
}

@article{Pestov3,
  author = {Vladimir G. Pestov},
  title = {A theorem of {Hrushovski--Solecki--Vershik} applied to uniform and coarse embeddings of the {Urysohn} metric space},
  journal = {Topology and its Applications},
  volume = {155},
  number = {14},
  pages = {1561--1575},
  year = {2008},
  doi = {10.1016/j.topol.2008.03.002}
}

@article{Sau,
  author = {Norbert W. Sauer},
  title = {Distance sets of {Urysohn} metric spaces},
  journal = {Canadian Journal of Mathematics},
  volume = {65},
  number = {1},
  pages = {222--240},
  year = {2013},
  doi = {10.4153/CJM-2012-022-4}
}

@incollection{Sau2,
  author = {Norbert W. Sauer},
  title = {Oscillation of {Urysohn} type spaces},
  booktitle = {Asymptotic Geometric Analysis},
  series = {Fields Institute Communications},
  volume = {68},
  pages = {247--270},
  publisher = {Springer},
  address = {New York},
  year = {2013},
  doi = {10.1007/978-1-4614-6406-8\_11}
}

@article{TZ,
  author = {Katrin Tent and Martin Ziegler},
  title = {On the isometry group of the {Urysohn} space},
  journal = {Journal of the London Mathematical Society},
  volume = {87},
  number = {1},
  pages = {289--303},
  year = {2013},
  doi = {10.1112/jlms/jds027}
}

@article{Ury1,
  author = {Paul Urysohn},
  title = {Sur un espace m\'{e}trique universel},
  journal = {Comptes Rendus de l'Acad\'{e}mie des Sciences de Paris},
  volume = {180},
  pages = {803--806},
  year = {1925}
}

@article{Ury2,
  author = {Paul Urysohn},
  title = {Sur un espace m\'{e}trique universel},
  journal = {Bulletin des Sciences Math\'{e}matiques, S\'{e}rie II},
  volume = {51},
  pages = {43--64, 74--90},
  year = {1927}
}

@article{Usp,
  author = {Vladimir V. Uspenskij},
  title = {On the group of isometries of the {Urysohn} universal metric space},
  journal = {Commentationes Mathematicae Universitatis Carolinae},
  volume = {31},
  number = {1},
  pages = {181--182},
  year = {1990}
}

@article{Usp2004,
  author = {Vladimir V. Uspenskij},
  title = {The {Urysohn} universal metric space is homeomorphic to a {Hilbert} space},
  journal = {Topology and its Applications},
  volume = {139},
  number = {1--3},
  pages = {145--149},
  year = {2004},
  doi = {10.1016/j.topol.2003.09.008}
}

@article{Ver0,
  author = {Anatoly M. Vershik},
  title = {The universal {Urysohn} space, Gromov metric triples and random metrics on the natural numbers},
  journal = {Russian Mathematical Surveys},
  volume = {53},
  number = {5},
  pages = {921--928},
  year = {1998},
  doi = {10.1070/RM1998v053n05ABEH000069}
}

@unpublished{Ver2002,
  author = {Anatoly M. Vershik},
  title = {Distance matrices, random metrics and {Urysohn} space},
  year = {2002},
  eprint = {math/0203008}
}

@article{Ver,
  author = {Anatoly M. Vershik},
  title = {Random metric spaces and universality},
  journal = {Russian Mathematical Surveys},
  volume = {59},
  number = {2},
  pages = {259--295},
  year = {2004},
  doi = {10.1070/RM2004v059n02ABEH000718}
}

@article{Wan,
  author = {Zhengchao Wan},
  title = {A novel construction of {Urysohn} universal ultrametric space via the {Gromov--{Hausdorff}} ultrametric},
  journal = {Topology and its Applications},
  volume = {300},
  pages = {107759},
  year = {2021},
  doi = {10.1016/j.topol.2021.107759},
  eprint = {2007.08105}
}

@misc{Mathoverflow,
  author = {Owen Sizemore},
  title = {Construction of a proper uncountable subgroup of $\mathbb{R}$ without Choice},
  year = {2010},
  note = {MathOverflow question and answers},
  url = {https://mathoverflow.net/questions/35970/construction-of-a-proper-uncountable-subgroup-of-mathbbr-without-choice}
}

@misc{denpaGR,
  author = {{Denpa Tsushin}},
  key = {Denpa Tsushin},
  title = {実数の閉部分群},
  year = {2016},
  note = {Denpa Tsushin (Hatena Blog), in Japanese},
  url = {http://concious4410.hatenablog.com/entry/2016/04/29/163931}
}

@misc{denpaAA,
  author = {{Denpa Tsushin}},
  key = {Denpa Tsushin},
  title = {アスコリアルツェラの定理},
  year = {2018},
  note = {Denpa Tsushin (Hatena Blog), in Japanese},
  url = {http://concious4410.hatenablog.com/entry/2018/03/29/154157}
}