Sequential definitions of compactness
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Date
2008
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
PERGAMON-ELSEVIER SCIENCE LTD
Access Rights
info:eu-repo/semantics/openAccess
Abstract
A subset F of a topological space is sequentially compact if any sequence x = (x(n)) of points in F has a convergent subsequence whose limit is in F. We say that a subset F of a topological group X is G-sequentially compact if any sequence x = (x(n)) of points in F has a convergent subsequence y such that G(y) is an element of F where G is an additive function from a subgroup of the group of all sequences of points in X. We investigate the impact of changing the definition of convergence of sequences on the structure of sequentially compactness of sets in the sense of G-sequential compactness. Sequential compactness is a special case of this generalization when G = lim. (C) 2007 Elsevier Ltd. All rights reserved.
Description
Keywords
sequences, series, summability, sequential compactness, countable compactness
Journal or Series
APPLIED MATHEMATICS LETTERS
WoS Q Value
Q2
Scopus Q Value
Q1
Volume
21
Issue
6
