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 Izv. Akad. Nauk SSSR Ser. Mat., 1979, Volume 43, Issue 2, Pages 442–478 (Mi izv1721)

On $\varkappa$-metrizable space

E. V. Shchepin

Abstract: In this paper the author studies spaces in which one can define a “distance” from points to canonically closed sets (the $\varkappa$-metric). It is proved that products of metric spaces and locally compact groups are examples of such spaces, and in these cases the $\varkappa$-metric can be constructed so that an analogue of the triangle axiom is satisfied. The topological structure of $\varkappa$-metrizable compact Hausdorff spaces is studied.
Bibliography: 26 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1980, 14:2, 407–440

Bibliographic databases:

UDC: 513.83
MSC: Primary 54D15, 54E35, 54E99; Secondary 28C10, 54A25, 54F05, 54B20, 54B35

Citation: E. V. Shchepin, “On $\varkappa$-metrizable space”, Izv. Akad. Nauk SSSR Ser. Mat., 43:2 (1979), 442–478; Math. USSR-Izv., 14:2 (1980), 407–440

Citation in format AMSBIB
\Bibitem{Shc79} \by E.~V.~Shchepin \paper On~$\varkappa$-metrizable space \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1979 \vol 43 \issue 2 \pages 442--478 \mathnet{http://mi.mathnet.ru/izv1721} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=534603} \zmath{https://zbmath.org/?q=an:0436.54024|0409.54040} \transl \jour Math. USSR-Izv. \yr 1980 \vol 14 \issue 2 \pages 407--440 \crossref{https://doi.org/10.1070/IM1980v014n02ABEH001124} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980KM96800012} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. E. V. Shchepin, “Functors and uncountable powers of compacta”, Russian Math. Surveys, 36:3 (1981), 1–71
2. A. Ch. Chigogidze, “On $\varkappa$-metrizable spaces”, Russian Math. Surveys, 37:2 (1982), 209–210
3. V. V. Uspenskii, “Topological groups and Dugundji compacta”, Math. USSR-Sb., 67:2 (1990), 555–580
4. V. V. Fedorchuk, “Probability measures in topology”, Russian Math. Surveys, 46:1 (1991), 45–93
5. Masami Sakai, “Non-(ω, ω1)-regular ultrafilters and perfect κ-normality of product spaces”, Topology and its Applications, 45:3 (1992), 165
6. HARUTO OHTA, MASAMI SAKAI, KEN-ICHI TAMANO, “Perfect ?-Normality of Product Spaces”, Ann N Y Acad Sci, 704:1 papers o (1993), 279
7. S. V. Lyudkovskii, “Topological groups and their $\varkappa$-metrics”, Russian Math. Surveys, 48:1 (1993), 178–179
8. W.W Comfort, F.Javier Trigos-Arrieta, “Locally pseudocompact topological groups”, Topology and its Applications, 62:3 (1995), 263
9. Masami Sakai, “Embeddings of κ-metrizable spaces into function spaces”, Topology and its Applications, 65:2 (1995), 155
10. V. V. Fedorchuk, “The Urysohn identity and dimension of manifolds”, Russian Math. Surveys, 53:5 (1998), 937–974
11. P.M. Gartside, “Nonstratifiability of topological vector spaces”, Topology and its Applications, 86:2 (1998), 133
12. Lutfi Kalantan, “Results about κ-normality”, Topology and its Applications, 125:1 (2002), 47
13. Lutfi Kalantan, Paul J. Szeptycki, “κ-normality and products of ordinals”, Topology and its Applications, 123:3 (2002), 537
14. A. V. Ivanov, “On the weight of nowhere dense subsets in compact spaces”, Siberian Math. J., 44:6 (2003), 991–996
15. M.G. Tkachenko, V.V. Tkachuk, “Dyadicity index and metrizability of compact continuous images of function spaces”, Topology and its Applications, 149:1-3 (2005), 243
16. S. V. Lyudkovskii, “Topologies and duality of $\kappa$-normed vector spaces”, Russian Math. Surveys, 61:3 (2006), 566–567
17. Masami Sakai, “Two properties of weaker than the Fréchet Urysohn property”, Topology and its Applications, 153:15 (2006), 2795
18. David Milovich, “Noetherian types of homogeneous compacta and dyadic compacta”, Topology and its Applications, 156:2 (2008), 443
19. M. Sanchis, “Moscow spaces and selection theory”, Topology and its Applications, 155:8 (2008), 883
20. K. L. Kozlov, V. A. Chatyrko, “Topological transformation groups and Dugundji compacta”, Sb. Math., 201:1 (2010), 103–128
21. D. Ipate, R. Lupu, “About rings of continuous functions in the expanded field of numbers”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2010, no. 1, 47–54
22. Paul Gartside, Michael Smith, “Counting the closed subgroups of profinite groups”, Journal of Group Theory, 13:1 (2010), 41
23. V. M. Valov, “Extenders and $\varkappa$-Metrizable Compacta”, Math. Notes, 89:3 (2011), 319–327
24. B. Berckmoes, R. Lowen, J. Van Casteren, “Distances on probability measures and random variables”, Journal of Mathematical Analysis and Applications, 374:2 (2011), 412
25. David Milovich, “The (λ,κ)-Freese-Nation Property for Boolean Algebras and Compacta”, Order, 29:2 (2012), 361
26. Fucai Lin, “Pseudocompact rectifiable spaces”, Topology and its Applications, 2014
27. Radul T., “Absolute Extensors and Binary Monads”, Appl. Categ. Struct., 25:2 (2017), 269–278
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