Sequential definitions of compactness
CitationÇakallı, H. (2008). Sequential definitions of compactness. Applied Mathematics Letters. ScienceDirect. 21(6), 594-598.
A subset of a topological space is sequentially compact if any sequence of points in has a convergent subsequence whose limit is in . We say that a subset of a topological group is -sequentially compact if any sequence of points in has a convergent subsequence such that where is an additive function from a subgroup of the group of all sequences of points in . We investigate the impact of changing the definition of convergence of sequences on the structure of sequentially compactness of sets in the sense of -sequential compactness. Sequential compactness is a special case of this generalization when .
SourceApplied Mathematics Letters
- Makale Koleksiyonu