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

This article is cited in 27 scientific papers (total in 27 papers)

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
Received: 02.06.1978

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
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\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
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\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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. Ch. Chigogidze, “On $\varkappa$-metrizable spaces”, Russian Math. Surveys, 37:2 (1982), 209–210  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. V. V. Uspenskii, “Topological groups and Dugundji compacta”, Math. USSR-Sb., 67:2 (1990), 555–580  mathnet  crossref  mathscinet  zmath  isi
    4. V. V. Fedorchuk, “Probability measures in topology”, Russian Math. Surveys, 46:1 (1991), 45–93  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. Masami Sakai, “Non-(ω, ω1)-regular ultrafilters and perfect κ-normality of product spaces”, Topology and its Applications, 45:3 (1992), 165  crossref
    6. HARUTO OHTA, MASAMI SAKAI, KEN-ICHI TAMANO, “Perfect ?-Normality of Product Spaces”, Ann N Y Acad Sci, 704:1 papers o (1993), 279  crossref  mathscinet  zmath
    7. S. V. Lyudkovskii, “Topological groups and their $\varkappa$-metrics”, Russian Math. Surveys, 48:1 (1993), 178–179  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. W.W Comfort, F.Javier Trigos-Arrieta, “Locally pseudocompact topological groups”, Topology and its Applications, 62:3 (1995), 263  crossref
    9. Masami Sakai, “Embeddings of κ-metrizable spaces into function spaces”, Topology and its Applications, 65:2 (1995), 155  crossref
    10. V. V. Fedorchuk, “The Urysohn identity and dimension of manifolds”, Russian Math. Surveys, 53:5 (1998), 937–974  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    11. P.M. Gartside, “Nonstratifiability of topological vector spaces”, Topology and its Applications, 86:2 (1998), 133  crossref
    12. Lutfi Kalantan, “Results about κ-normality”, Topology and its Applications, 125:1 (2002), 47  crossref
    13. Lutfi Kalantan, Paul J. Szeptycki, “κ-normality and products of ordinals”, Topology and its Applications, 123:3 (2002), 537  crossref
    14. A. V. Ivanov, “On the weight of nowhere dense subsets in compact spaces”, Siberian Math. J., 44:6 (2003), 991–996  mathnet  crossref  mathscinet  zmath  isi  elib
    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  crossref
    16. S. V. Lyudkovskii, “Topologies and duality of $\kappa$-normed vector spaces”, Russian Math. Surveys, 61:3 (2006), 566–567  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    17. Masami Sakai, “Two properties of weaker than the Fréchet Urysohn property”, Topology and its Applications, 153:15 (2006), 2795  crossref
    18. David Milovich, “Noetherian types of homogeneous compacta and dyadic compacta”, Topology and its Applications, 156:2 (2008), 443  crossref
    19. M. Sanchis, “Moscow spaces and selection theory”, Topology and its Applications, 155:8 (2008), 883  crossref
    20. K. L. Kozlov, V. A. Chatyrko, “Topological transformation groups and Dugundji compacta”, Sb. Math., 201:1 (2010), 103–128  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    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  mathnet  mathscinet  zmath
    22. Paul Gartside, Michael Smith, “Counting the closed subgroups of profinite groups”, Journal of Group Theory, 13:1 (2010), 41  crossref
    23. V. M. Valov, “Extenders and $\varkappa$-Metrizable Compacta”, Math. Notes, 89:3 (2011), 319–327  mathnet  crossref  crossref  mathscinet
    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  crossref
    25. David Milovich, “The (λ,κ)-Freese-Nation Property for Boolean Algebras and Compacta”, Order, 29:2 (2012), 361  crossref
    26. Fucai Lin, “Pseudocompact rectifiable spaces”, Topology and its Applications, 2014  crossref
    27. Radul T., “Absolute Extensors and Binary Monads”, Appl. Categ. Struct., 25:2 (2017), 269–278  crossref  isi
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