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Proceedings of the American Mathematical Society

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Finite-to-one maps and open extensions of maps


Author: J. K. Kohli
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
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 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
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  • 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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Keywords: <IMG WIDTH="16" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$p$">-space, feathering, weight, singular point, Stone-&#268;ech compactification
Article copyright: © Copyright 1975 American Mathematical Society