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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Convergence properties of neighboring sequences
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by Ralph R. Sabella
Proc. Amer. Math. Soc. 38 (1973), 405-409
DOI: https://doi.org/10.1090/S0002-9939-1973-0312479-8

Abstract:

First countable spaces and semimetrizable spaces are examples of topological spaces which can be characterized in terms of convergence properties of sequences “neighboring” a point. In this paper we consider conditions sufficient for metrizability of spaces defined in terms of convergence properties of “neighboring” sequences, in particular, those in which the set of cluster points of one sequence is a subset of that of any “neighboring” sequence. The special case in which the sets of cluster points are equal is shown to be a characterization of metrizability in ${T_0}$-spaces.
References
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Bibliographic Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 38 (1973), 405-409
  • MSC: Primary 54E35
  • DOI: https://doi.org/10.1090/S0002-9939-1973-0312479-8
  • MathSciNet review: 0312479