Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54E35

Retrieve articles in all journals with MSC: 54E35


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

American Mathematical Society