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Sequential definitions of compactness

✍ Scribed by H. Çakalli

Book ID
104000408
Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
186 KB
Volume
21
Category
Article
ISSN
0893-9659

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✦ Synopsis

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) ∈ 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.

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