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Convergence Formulas for Sequences of Sets

Published online by Cambridge University Press:  20 November 2018

Frank A. Chimenti
Frank A. Chimenti*
Affiliation:
State University College, Fredonia, New York
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This paper is concerned with the convergence of sequences of subsets of a topological space, as defined by F. Hausdorff [6]. Such a sequence converges if and only if its limit inferior equals its limit superior, where its limit inferior (respectively, superior) is that set each of whose elements satisfies the condition that each of its neighborhoods has nonempty intersection with all but finitely (respectively, with infinitely) many terms of the sequence.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 5 , 01 October 1975 , pp. 961 - 969
Copyright
Copyright © Canadian Mathematical Society 1975

References

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