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A note on Ščepin's theorem


Author: Kōichi Tsuda
Journal: Proc. Amer. Math. Soc. 91 (1984), 167-170
MSC: Primary 54C55; Secondary 54B35, 54D18, 54E18, 54F15, 54F45
DOI: https://doi.org/10.1090/S0002-9939-1984-0735586-1
MathSciNet review: 735586
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Abstract | References | Similar Articles | Additional Information

Abstract: We shall generalize a theorem of Ščepin as follows.

Theorem. Every finite dimensional $ {\text{ANR}}({\mathcal{P}_1})$ is metrizable, where $ {\mathcal{P}_1}$ denotes the class of all $ \sigma $-locally compact, paracompact $ p$-spaces.


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  • [1] R. Engelking, General topology, PWN, Warsaw, 1977. MR 0500780 (58:18316b)
  • [2] S. T. Hu, Theory of retracts, Wayne State Univ. Press, Detroit, Mich., 1965 MR 0181977 (31:6202)
  • [3] Ju. T. Lisica, Extension of continuous mappings and factorization theorem, Sibirsk. Mat. Ž. 14 (1973), 128-139 = Siberian Math. J. 18 (1977), 90-96. MR 0326647 (48:4990)
  • [4] S. Mardešič and A. Šostak, On the homotopy type of ANR's for $ p$-paracompacta, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 27 (1979), 803-808. MR 603152 (82e:54018)
  • [5] J. Nagata, A note on $ M$-spaces and topologically complete spaces, Proc. Japan Acad. 45 (1969), 541-543. MR 0254803 (40:8010)
  • [6] A. Okuyama, Some generalizations of metric spaces, their metrization theorems and product spaces, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 9 (1967), 236-254. MR 0230283 (37:5846)
  • [7] H. Potoczny, Closure-preserving families of compact sets, General Topology and Appl. 3 (1973), 243-248. MR 0322805 (48:1166)
  • [8] T. Przymusiński, Collectionwise normality and absolute retracts, Fund. Math. 98 (1977), 61-73. MR 528355 (80g:54021a)
  • [9] E. V. Ščepin, Every finite-dimensional compact absolute neighborhood retract is metrizable, Dokl. Akad. Nauk SSSR 233 (1977), 304-307=Soviet Math. Dokl. 18 (1977), 402-406. MR 0487966 (58:7545)
  • [10] -, Sur les applications contiues des cubes de Tihonov, C. R. Acad. Sci. Paris Sér. A-B 288 (1979), 257-260. MR 524787 (80b:54007)
  • [11] R. Telgársky, $ C$-scattered and paramcompact spaces, Fund. Math. 73 (1971), 59-74.
  • [12] -, Spaces defined by topological games, Fund. Math. 88 (1975), 192-223. MR 0380708 (52:1605)
  • [13] -, A letter to the author on March 8, 1983.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0735586-1
Keywords: ANR, paracompact $ p$-space, generalized Peano continuum
Article copyright: © Copyright 1984 American Mathematical Society

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