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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Finite-to-one maps and open extensions of maps
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by J. K. Kohli PDF
Proc. Amer. Math. Soc. 48 (1975), 464-468 Request permission

Abstract:

In the class of $p$-spaces it is shown that (a) infinite weight is not lowered by finite-to-one maps which are open except at finitely many points, (b) metrizability is inversely preserved under finite-to-one maps which are open except at finitely many points.
References
  • A. Archangelski, Concerning the weight of topological spaces, General Topology and its Relations to Modern Analysis and Algebra (Proc. Sympos., Prague, 1961) Academic Press, New York; Publ. House Czech. Acad. Sci., Prague, 1962, pp. 72–74. MR 0174030
  • —, On a class of spaces containing all locally bicompact and all metric spaces, Mat. Sb. 67 (109) (1965), 55-85; English transl., Amer. Math. Soc. Transl. (2) 92 (1970), 1-39. MR 32 #8299; 42 #3.
  • M. M. Čoban, Finite-to-one open maps, Dokl. Akad. Nauk SSSR 174 (1967), 41–44 (Russian). MR 0215286
  • S. P. Franklin and J. K. Kohli, On open extensions of maps, Canadian J. Math. 22 (1970), 691–696. MR 264626, DOI 10.4153/CJM-1970-077-5
  • J. K. Kohli, Open extensions of maps, finite-to-one maps and dimension (preprint).
  • V. V. Proizvolov, On finite-to-one open mappings, Dokl. Akad. Nauk SSSR 166 (1966), 38–40 (Russian). MR 0188991
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 48 (1975), 464-468
  • MSC: Primary 54C10; Secondary 54E10
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0370472-5
  • MathSciNet review: 0370472