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Convergence properties of neighboring sequences


Author: Ralph R. Sabella
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
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0312479-8
Keywords: Open neighborhood assignments, $ U$-linked sequences, coconvergent, contraconvergent, Moore Metrization Theorem
Article copyright: © Copyright 1973 American Mathematical Society

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