
This article is cited in 18 scientific papers (total in 18 papers)
On some topological spaces that occur in functional analysis
A. V. Arkhangel'skii^{}
Abstract:
This is a study of the topological properties of spaces of continuous real functions on compact sets in the topology of pointwise convergence. Compact subsets in these spaces are called functionally complete. The topological properties of functionally complete compacta are established, among them the fact that the density of each subspace of a functionally complete compactum is equal to its weight. Compacta of countable tightness having this last property are called exact. Each functionally complete compactum is exact. It is proved that each exact compactum is a Fréchet–Uryson space and satisfies the first axiom of countability on an everywhere dense set of points. The continuous image of an exact compactum is exact. Recently M. Vage has constructed a “naive” example of an exact but not functionally complete compact space. Another interesting question is: does there exist a nonmetrizable, homogeneous, functionally complete compactum?
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Russian Mathematical Surveys, 1976, 31:5, 14–30
Bibliographic databases:
UDC:
513.831
MSC: 46A19, 46A50 Received: 27.05.1976
Citation:
A. V. Arkhangel'skii, “On some topological spaces that occur in functional analysis”, Uspekhi Mat. Nauk, 31:5(191) (1976), 17–32; Russian Math. Surveys, 31:5 (1976), 14–30
Citation in format AMSBIB
\Bibitem{Ark76}
\by A.~V.~Arkhangel'skii
\paper On some topological spaces that occur in functional analysis
\jour Uspekhi Mat. Nauk
\yr 1976
\vol 31
\issue 5(191)
\pages 1732
\mathnet{http://mi.mathnet.ru/umn3840}
\mathscinet{http://www.ams.org/mathscinetgetitem?mr=458366}
\zmath{https://zbmath.org/?q=an:0344.460580358.46019}
\transl
\jour Russian Math. Surveys
\yr 1976
\vol 31
\issue 5
\pages 1430
\crossref{https://doi.org/10.1070/RM1976v031n05ABEH004183}
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Yu. A. Abramovich, “On a new class of Fréchet–Urysohn spaces”, Russian Math. Surveys, 33:5 (1978), 177–178

A. V. Arkhangel'skii, “Structure and classification of topological spaces and cardinal invariants”, Russian Math. Surveys, 33:6 (1978), 33–96

S. P. Gul'ko, “On the structure of spaces of continuous functions and their complete paracompactness”, Russian Math. Surveys, 34:6 (1979), 36–44

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E. G. Pytkeev, “On the tightness of spaces of continuous functions”, Russian Math. Surveys, 37:1 (1982), 176–177

A. V. Arkhangel'skii, “Function spaces in the topology of pointwise convergence, and compact sets”, Russian Math. Surveys, 39:5 (1984), 9–56

A. V. Arkhangel'skii, “Topological homogeneity. Topological groups and their continuous images”, Russian Math. Surveys, 42:2 (1987), 83–131

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