Metric space (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Metric space" in English language version.

refsWebsite

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20doi.org

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2warwick.ac.uk

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1helsinki.fi

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1psu.edu

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1mta.ca

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ams.org

mathscinet.ams.org

Steen & Seebach (1995); Smyth (1988) Steen, Lynn Arthur; Seebach, J. Arthur Jr. (1995) [1978]. Counterexamples in Topology. Dover. ISBN 978-0-486-68735-3. MR 0507446. Smyth, M. (1988), "Quasi uniformities: reconciling domains with metric spaces", in Main, M.; Melton, A.; Mislove, M.; Schmidt, D. (eds.), Mathematical Foundations of Programming Language Semantics, Lecture Notes in Computer Science, vol. 298, Springer-Verlag, pp. 236–253, doi:10.1007/3-540-19020-1_12, ISBN 978-3-540-19020-2
Väisälä 2005. Väisälä, Jussi (2005). "Gromov hyperbolic spaces" (PDF). Expositiones Mathematicae. 23 (3): 187–231. doi:10.1016/j.exmath.2005.01.010. MR 2164775.
Buldygin & Kozachenko 2000. Buldygin, V. V.; Kozachenko, Yu. V. (2000), Metric Characterization of Random Variables and Random Processes, Translations of Mathematical Monographs, vol. 188, Providence, Rhode Island: American Mathematical Society, p. 129, doi:10.1090/mmono/188, ISBN 0-8218-0533-9, MR 1743716
Helemskii 2006. Helemskii, A. Ya. (2006), Lectures and Exercises on Functional Analysis, Translations of Mathematical Monographs, vol. 233, Providence, Rhode Island: American Mathematical Society, p. 14, doi:10.1090/mmono/233, ISBN 978-0-8218-4098-6, MR 2248303
Arkhangel'skii & Pontryagin (1990); Aldrovandi & Pereira (2017) Arkhangel'skii, A. V.; Pontryagin, L. S. (1990), General Topology I: Basic Concepts and Constructions Dimension Theory, Encyclopaedia of Mathematical Sciences, Springer, ISBN 3-540-18178-4 Aldrovandi, Ruben; Pereira, José Geraldo (2017), An Introduction to Geometrical Physics (2nd ed.), Hackensack, New Jersey: World Scientific, p. 20, ISBN 978-981-3146-81-5, MR 3561561
Deza & Laurent 1997. Deza, Michel Marie; Laurent, Monique (1997), Geometry of Cuts and Metrics, Algorithms and Combinatorics, vol. 15, Springer-Verlag, Berlin, p. 27, doi:10.1007/978-3-642-04295-9, ISBN 3-540-61611-X, MR 1460488
Lawvere (1973); Vickers (2005) Lawvere, F. William (December 1973). "Metric spaces, generalized logic, and closed categories". Rendiconti del Seminario Matematico e Fisico di Milano. 43 (1): 135–166. doi:10.1007/BF02924844. S2CID 1845177. Vickers, Steven (2005). "Localic completion of generalized metric spaces, I". Theory and Applications of Categories. 14 (15): 328–356. MR 2182680.

arxiv.org

Gigli, Nicola (2018-10-18). "Lecture notes on differential calculus on RCD spaces". Publications of the Research Institute for Mathematical Sciences. 54 (4): 855–918. arXiv:1703.06829. doi:10.4171/PRIMS/54-4-4. S2CID 119129867.
Linial, Nathan (2003). "Finite metric-spaces—combinatorics, geometry and algorithms". Proceedings of the ICM, Beijing 2002. Vol. 3. pp. 573–586. arXiv:math/0304466.
Gottlieb, Lee-Ad; Solomon, Shay (2014-06-08). Light spanners for snowflake metrics. SOCG '14: Proceedings of the thirtieth annual symposium on Computational geometry. pp. 387–395. arXiv:1401.5014. doi:10.1145/2582112.2582140.
Xia 2009. Xia, Q. (2009). "The geodesic problem in quasimetric spaces". Journal of Geometric Analysis. 19 (2): 452–479. arXiv:0807.3377. doi:10.1007/s12220-008-9065-4. S2CID 17475581.
Xia 2008. Xia, Qinglan (2008). "The geodesic problem in nearmetric spaces". Journal of Geometric Analysis. 19 (2): 452–479. arXiv:0807.3377. doi:10.1007/s12220-008-9065-4. S2CID 17475581.
Vitányi 2011. Vitányi, Paul M. B. (2011). "Information distance in multiples". IEEE Transactions on Information Theory. 57 (4): 2451–2456. arXiv:0905.3347. doi:10.1109/TIT.2011.2110130. S2CID 6302496.
Cohen & Vitányi 2012. Cohen, Andrew R.; Vitányi, Paul M. B. (2012), "Normalized compression distance of multisets with applications", IEEE Transactions on Pattern Analysis and Machine Intelligence, 37 (8): 1602–1614, arXiv:1212.5711, doi:10.1109/TPAMI.2014.2375175, PMC 4566858, PMID 26352998

books.google.com

Buldygin & Kozachenko 2000. Buldygin, V. V.; Kozachenko, Yu. V. (2000), Metric Characterization of Random Variables and Random Processes, Translations of Mathematical Monographs, vol. 188, Providence, Rhode Island: American Mathematical Society, p. 129, doi:10.1090/mmono/188, ISBN 0-8218-0533-9, MR 1743716
Helemskii 2006. Helemskii, A. Ya. (2006), Lectures and Exercises on Functional Analysis, Translations of Mathematical Monographs, vol. 233, Providence, Rhode Island: American Mathematical Society, p. 14, doi:10.1090/mmono/233, ISBN 978-0-8218-4098-6, MR 2248303
Arkhangel'skii & Pontryagin (1990); Aldrovandi & Pereira (2017) Arkhangel'skii, A. V.; Pontryagin, L. S. (1990), General Topology I: Basic Concepts and Constructions Dimension Theory, Encyclopaedia of Mathematical Sciences, Springer, ISBN 3-540-18178-4 Aldrovandi, Ruben; Pereira, José Geraldo (2017), An Introduction to Geometrical Physics (2nd ed.), Hackensack, New Jersey: World Scientific, p. 20, ISBN 978-981-3146-81-5, MR 3561561
Deza & Laurent 1997. Deza, Michel Marie; Laurent, Monique (1997), Geometry of Cuts and Metrics, Algorithms and Combinatorics, vol. 15, Springer-Verlag, Berlin, p. 27, doi:10.1007/978-3-642-04295-9, ISBN 3-540-61611-X, MR 1460488

cuni.cz

kam.mff.cuni.cz

Jiří Matoušek and Assaf Naor, ed. "Open problems on embeddings of finite metric spaces". Archived 2010-12-26 at the Wayback Machine.

doi.org

Gleason, Andrew (1991). Fundamentals of Abstract Analysis (1st ed.). Taylor & Francis. p. 223. doi:10.1201/9781315275444. ISBN 9781315275444. S2CID 62222843.
Fréchet, M. (December 1906). "Sur quelques points du calcul fonctionnel". Rendiconti del Circolo Matematico di Palermo. 22 (1): 1–72. doi:10.1007/BF03018603. S2CID 123251660.
Blumberg, Henry (1927). "Hausdorff's Grundzüge der Mengenlehre". Bulletin of the American Mathematical Society. 6: 778–781. doi:10.1090/S0002-9904-1920-03378-1.
Heinonen 2007, p. 191. Heinonen, Juha (2007-01-24). "Nonsmooth calculus". Bulletin of the American Mathematical Society. 44 (2): 163–232. doi:10.1090/S0273-0979-07-01140-8.
Gigli, Nicola (2018-10-18). "Lecture notes on differential calculus on RCD spaces". Publications of the Research Institute for Mathematical Sciences. 54 (4): 855–918. arXiv:1703.06829. doi:10.4171/PRIMS/54-4-4. S2CID 119129867.
Bourgain, J. (1985). "On lipschitz embedding of finite metric spaces in Hilbert space". Israel Journal of Mathematics. 52 (1–2): 46–52. doi:10.1007/BF02776078. S2CID 121649019.
Gottlieb, Lee-Ad; Solomon, Shay (2014-06-08). Light spanners for snowflake metrics. SOCG '14: Proceedings of the thirtieth annual symposium on Computational geometry. pp. 387–395. arXiv:1401.5014. doi:10.1145/2582112.2582140.
Robinson, D.F.; Foulds, L.R. (February 1981). "Comparison of phylogenetic trees". Mathematical Biosciences. 53 (1–2): 131–147. doi:10.1016/0025-5564(81)90043-2. S2CID 121156920.
Steen & Seebach (1995); Smyth (1988) Steen, Lynn Arthur; Seebach, J. Arthur Jr. (1995) [1978]. Counterexamples in Topology. Dover. ISBN 978-0-486-68735-3. MR 0507446. Smyth, M. (1988), "Quasi uniformities: reconciling domains with metric spaces", in Main, M.; Melton, A.; Mislove, M.; Schmidt, D. (eds.), Mathematical Foundations of Programming Language Semantics, Lecture Notes in Computer Science, vol. 298, Springer-Verlag, pp. 236–253, doi:10.1007/3-540-19020-1_12, ISBN 978-3-540-19020-2
Väisälä 2005. Väisälä, Jussi (2005). "Gromov hyperbolic spaces" (PDF). Expositiones Mathematicae. 23 (3): 187–231. doi:10.1016/j.exmath.2005.01.010. MR 2164775.
Bukatin, Michael; Kopperman, Ralph; Matthews, Steve; Pajoohesh, Homeira (2009-10-01). "Partial Metric Spaces" (PDF). American Mathematical Monthly. 116 (8): 708–718. doi:10.4169/193009709X460831. S2CID 13969183.
Xia 2009. Xia, Q. (2009). "The geodesic problem in quasimetric spaces". Journal of Geometric Analysis. 19 (2): 452–479. arXiv:0807.3377. doi:10.1007/s12220-008-9065-4. S2CID 17475581.
Xia 2008. Xia, Qinglan (2008). "The geodesic problem in nearmetric spaces". Journal of Geometric Analysis. 19 (2): 452–479. arXiv:0807.3377. doi:10.1007/s12220-008-9065-4. S2CID 17475581.
Fraigniaud, Lebhar & Viennot 2008. Fraigniaud, P.; Lebhar, E.; Viennot, L. (2008), "The inframetric model for the internet", 2008 IEEE INFOCOM - The 27th Conference on Computer Communications, pp. 1085–1093, CiteSeerX 10.1.1.113.6748, doi:10.1109/INFOCOM.2008.163, ISBN 978-1-4244-2026-1, S2CID 5733968
Buldygin & Kozachenko 2000. Buldygin, V. V.; Kozachenko, Yu. V. (2000), Metric Characterization of Random Variables and Random Processes, Translations of Mathematical Monographs, vol. 188, Providence, Rhode Island: American Mathematical Society, p. 129, doi:10.1090/mmono/188, ISBN 0-8218-0533-9, MR 1743716
Helemskii 2006. Helemskii, A. Ya. (2006), Lectures and Exercises on Functional Analysis, Translations of Mathematical Monographs, vol. 233, Providence, Rhode Island: American Mathematical Society, p. 14, doi:10.1090/mmono/233, ISBN 978-0-8218-4098-6, MR 2248303
Deza & Laurent 1997. Deza, Michel Marie; Laurent, Monique (1997), Geometry of Cuts and Metrics, Algorithms and Combinatorics, vol. 15, Springer-Verlag, Berlin, p. 27, doi:10.1007/978-3-642-04295-9, ISBN 3-540-61611-X, MR 1460488
Lawvere (1973); Vickers (2005) Lawvere, F. William (December 1973). "Metric spaces, generalized logic, and closed categories". Rendiconti del Seminario Matematico e Fisico di Milano. 43 (1): 135–166. doi:10.1007/BF02924844. S2CID 1845177. Vickers, Steven (2005). "Localic completion of generalized metric spaces, I". Theory and Applications of Categories. 14 (15): 328–356. MR 2182680.
Vitányi 2011. Vitányi, Paul M. B. (2011). "Information distance in multiples". IEEE Transactions on Information Theory. 57 (4): 2451–2456. arXiv:0905.3347. doi:10.1109/TIT.2011.2110130. S2CID 6302496.
Cohen & Vitányi 2012. Cohen, Andrew R.; Vitányi, Paul M. B. (2012), "Normalized compression distance of multisets with applications", IEEE Transactions on Pattern Analysis and Machine Intelligence, 37 (8): 1602–1614, arXiv:1212.5711, doi:10.1109/TPAMI.2014.2375175, PMC 4566858, PMID 26352998

elsevier.com

linkinghub.elsevier.com

Robinson, D.F.; Foulds, L.R. (February 1981). "Comparison of phylogenetic trees". Mathematical Biosciences. 53 (1–2): 131–147. doi:10.1016/0025-5564(81)90043-2. S2CID 121156920.

google.com

Margalit & Thomas 2017. Margalit, Dan; Thomas, Anne (2017). "Office Hour 7. Quasi-isometries". Office hours with a geometric group theorist. Princeton University Press. pp. 125–145. ISBN 978-1-4008-8539-8. JSTOR j.ctt1vwmg8g.11.

helsinki.fi

Väisälä 2005. Väisälä, Jussi (2005). "Gromov hyperbolic spaces" (PDF). Expositiones Mathematicae. 23 (3): 187–231. doi:10.1016/j.exmath.2005.01.010. MR 2164775.

jstor.org

Rudin, Mary Ellen. A new proof that metric spaces are paracompact Archived 2016-04-12 at the Wayback Machine. Proceedings of the American Mathematical Society, Vol. 20, No. 2. (Feb., 1969), p. 603.
Margalit & Thomas 2017. Margalit, Dan; Thomas, Anne (2017). "Office Hour 7. Quasi-isometries". Office hours with a geometric group theorist. Princeton University Press. pp. 125–145. ISBN 978-1-4008-8539-8. JSTOR j.ctt1vwmg8g.11.

mta.ca

tac.mta.ca

Lawvere (1973); Vickers (2005) Lawvere, F. William (December 1973). "Metric spaces, generalized logic, and closed categories". Rendiconti del Seminario Matematico e Fisico di Milano. 43 (1): 135–166. doi:10.1007/BF02924844. S2CID 1845177. Vickers, Steven (2005). "Localic completion of generalized metric spaces, I". Theory and Applications of Categories. 14 (15): 328–356. MR 2182680.

nih.gov

ncbi.nlm.nih.gov

Cohen & Vitányi 2012. Cohen, Andrew R.; Vitányi, Paul M. B. (2012), "Normalized compression distance of multisets with applications", IEEE Transactions on Pattern Analysis and Machine Intelligence, 37 (8): 1602–1614, arXiv:1212.5711, doi:10.1109/TPAMI.2014.2375175, PMC 4566858, PMID 26352998

pubmed.ncbi.nlm.nih.gov

Cohen & Vitányi 2012. Cohen, Andrew R.; Vitányi, Paul M. B. (2012), "Normalized compression distance of multisets with applications", IEEE Transactions on Pattern Analysis and Machine Intelligence, 37 (8): 1602–1614, arXiv:1212.5711, doi:10.1109/TPAMI.2014.2375175, PMC 4566858, PMID 26352998

oapen.org

library.oapen.org

Hitzler & Seda 2016, Definition 4.3.1. Hitzler, Pascal; Seda, Anthony (2016-04-19). Mathematical Aspects of Logic Programming Semantics. CRC Press. ISBN 978-1-4398-2962-2.
Hitzler & Seda 2016, Definition 4.2.1. Hitzler, Pascal; Seda, Anthony (2016-04-19). Mathematical Aspects of Logic Programming Semantics. CRC Press. ISBN 978-1-4398-2962-2.

psu.edu

citeseerx.ist.psu.edu

Fraigniaud, Lebhar & Viennot 2008. Fraigniaud, P.; Lebhar, E.; Viennot, L. (2008), "The inframetric model for the internet", 2008 IEEE INFOCOM - The 27th Conference on Computer Communications, pp. 1085–1093, CiteSeerX 10.1.1.113.6748, doi:10.1109/INFOCOM.2008.163, ISBN 978-1-4244-2026-1, S2CID 5733968

semanticscholar.org

api.semanticscholar.org

Gleason, Andrew (1991). Fundamentals of Abstract Analysis (1st ed.). Taylor & Francis. p. 223. doi:10.1201/9781315275444. ISBN 9781315275444. S2CID 62222843.
Fréchet, M. (December 1906). "Sur quelques points du calcul fonctionnel". Rendiconti del Circolo Matematico di Palermo. 22 (1): 1–72. doi:10.1007/BF03018603. S2CID 123251660.
Gigli, Nicola (2018-10-18). "Lecture notes on differential calculus on RCD spaces". Publications of the Research Institute for Mathematical Sciences. 54 (4): 855–918. arXiv:1703.06829. doi:10.4171/PRIMS/54-4-4. S2CID 119129867.
Bourgain, J. (1985). "On lipschitz embedding of finite metric spaces in Hilbert space". Israel Journal of Mathematics. 52 (1–2): 46–52. doi:10.1007/BF02776078. S2CID 121649019.
Robinson, D.F.; Foulds, L.R. (February 1981). "Comparison of phylogenetic trees". Mathematical Biosciences. 53 (1–2): 131–147. doi:10.1016/0025-5564(81)90043-2. S2CID 121156920.
Bukatin, Michael; Kopperman, Ralph; Matthews, Steve; Pajoohesh, Homeira (2009-10-01). "Partial Metric Spaces" (PDF). American Mathematical Monthly. 116 (8): 708–718. doi:10.4169/193009709X460831. S2CID 13969183.
Xia 2009. Xia, Q. (2009). "The geodesic problem in quasimetric spaces". Journal of Geometric Analysis. 19 (2): 452–479. arXiv:0807.3377. doi:10.1007/s12220-008-9065-4. S2CID 17475581.
Xia 2008. Xia, Qinglan (2008). "The geodesic problem in nearmetric spaces". Journal of Geometric Analysis. 19 (2): 452–479. arXiv:0807.3377. doi:10.1007/s12220-008-9065-4. S2CID 17475581.
Fraigniaud, Lebhar & Viennot 2008. Fraigniaud, P.; Lebhar, E.; Viennot, L. (2008), "The inframetric model for the internet", 2008 IEEE INFOCOM - The 27th Conference on Computer Communications, pp. 1085–1093, CiteSeerX 10.1.1.113.6748, doi:10.1109/INFOCOM.2008.163, ISBN 978-1-4244-2026-1, S2CID 5733968
Lawvere (1973); Vickers (2005) Lawvere, F. William (December 1973). "Metric spaces, generalized logic, and closed categories". Rendiconti del Seminario Matematico e Fisico di Milano. 43 (1): 135–166. doi:10.1007/BF02924844. S2CID 1845177. Vickers, Steven (2005). "Localic completion of generalized metric spaces, I". Theory and Applications of Categories. 14 (15): 328–356. MR 2182680.
Vitányi 2011. Vitányi, Paul M. B. (2011). "Information distance in multiples". IEEE Transactions on Information Theory. 57 (4): 2451–2456. arXiv:0905.3347. doi:10.1109/TIT.2011.2110130. S2CID 6302496.

warwick.ac.uk

dcs.warwick.ac.uk

"Partial metrics: welcome". www.dcs.warwick.ac.uk. Archived from the original on 2017-07-27. Retrieved 2018-05-02.
Bukatin, Michael; Kopperman, Ralph; Matthews, Steve; Pajoohesh, Homeira (2009-10-01). "Partial Metric Spaces" (PDF). American Mathematical Monthly. 116 (8): 708–718. doi:10.4169/193009709X460831. S2CID 13969183.

web.archive.org

Rudin, Mary Ellen. A new proof that metric spaces are paracompact Archived 2016-04-12 at the Wayback Machine. Proceedings of the American Mathematical Society, Vol. 20, No. 2. (Feb., 1969), p. 603.
Jiří Matoušek and Assaf Naor, ed. "Open problems on embeddings of finite metric spaces". Archived 2010-12-26 at the Wayback Machine.
Goreham, Anthony. Sequential convergence in Topological Spaces Archived 2011-06-04 at the Wayback Machine. Honours' Dissertation, Queen's College, Oxford (April, 2001), p. 14
"Partial metrics: welcome". www.dcs.warwick.ac.uk. Archived from the original on 2017-07-27. Retrieved 2018-05-02.

worldcat.org

Rudin 1976, p. 30. Rudin, Walter (1976). Principles of Mathematical Analysis (Third ed.). New York: McGraw-Hill. ISBN 0-07-054235-X. OCLC 1502474.
Burago, Burago & Ivanov 2001, p. 2.
Some authors refer to any distance-preserving function as an isometry, e.g. Munkres 2000, p. 181. Burago, Dmitri; Burago, Yuri; Ivanov, Sergei (2001). A course in metric geometry. Providence, RI: American Mathematical Society. ISBN 0-8218-2129-6. Munkres, James R. (2000). Topology (Second ed.). Upper Saddle River, NJ: Prentice Hall, Inc. ISBN 978-0-13-181629-9. OCLC 42683260.
Narici & Beckenstein 2011, pp. 47–66. Narici, Lawrence; Beckenstein, Edward (2011), Topological Vector Spaces, Pure and applied mathematics (Second ed.), Boca Raton, FL: CRC Press, ISBN 978-1584888666, OCLC 144216834

yorku.ca

at.yorku.ca

Goreham, Anthony. Sequential convergence in Topological Spaces Archived 2011-06-04 at the Wayback Machine. Honours' Dissertation, Queen's College, Oxford (April, 2001), p. 14

zenodo.org

Fréchet, M. (December 1906). "Sur quelques points du calcul fonctionnel". Rendiconti del Circolo Matematico di Palermo. 22 (1): 1–72. doi:10.1007/BF03018603. S2CID 123251660.