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 Uspekhi Mat. Nauk, 1976, Volume 31, Issue 5(191), Pages 17–32 (Mi umn3840)

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 non-metrizable, homogeneous, functionally complete compactum?

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English version:
Russian Mathematical Surveys, 1976, 31:5, 14–30

Bibliographic databases:

UDC: 513.831
MSC: 46A19, 46A50

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 17--32 \mathnet{http://mi.mathnet.ru/umn3840} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=458366} \zmath{https://zbmath.org/?q=an:0344.46058|0358.46019} \transl \jour Russian Math. Surveys \yr 1976 \vol 31 \issue 5 \pages 14--30 \crossref{https://doi.org/10.1070/RM1976v031n05ABEH004183} 

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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. Yu. A. Abramovich, “On a new class of Fréchet–Urysohn spaces”, Russian Math. Surveys, 33:5 (1978), 177–178
2. A. V. Arkhangel'skii, “Structure and classification of topological spaces and cardinal invariants”, Russian Math. Surveys, 33:6 (1978), 33–96
3. S. P. Gul'ko, “On the structure of spaces of continuous functions and their complete paracompactness”, Russian Math. Surveys, 34:6 (1979), 36–44
4. Mohammad Ismail, Peter Nyikos, “On spaces in which countably compact sets are closed, and hereditary properties”, Topology and its Applications, 11:3 (1980), 281
5. E. G. Pytkeev, “On the tightness of spaces of continuous functions”, Russian Math. Surveys, 37:1 (1982), 176–177
6. A. V. Arkhangel'skii, “Function spaces in the topology of pointwise convergence, and compact sets”, Russian Math. Surveys, 39:5 (1984), 9–56
7. A. V. Arkhangel'skii, “Topological homogeneity. Topological groups and their continuous images”, Russian Math. Surveys, 42:2 (1987), 83–131
8. O.G. Okunev, “On Lindelöf Σ-spaces of continuous functions in the pointwise topology”, Topology and its Applications, 49:2 (1993), 149
9. Toshihiro Nagamizu, “A note on fragmentable topological spaces”, BAZ, 49:1 (1994), 91
10. M. Bell, “The hyperspace of a compact space, I”, Topology and its Applications, 72:1 (1996), 39
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13. H.J.K. Junnila, “Embeddings of Weakly Compact Sets and *-Paired Banach Spaces”, Journal of Functional Analysis, 177:2 (2000), 442
14. Oleg Okunev, Angel Tamariz-Mascarúa, “On the Čech number of Cp(X)”, Topology and its Applications, 137:1-3 (2004), 237
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17. A. Dow, H. Junnila, J. Pelant, “Chain conditions and weak topologies”, Topology and its Applications, 156:7 (2009), 1327
18. B. Cascales, M. Muñoz, J. Orihuela, “The number of K-determination of topological spaces”, RACSAM, 2012
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