Sequential definitions of compactness
Applied Mathematics Letters, cilt.21, sa.6, ss.594-598, 2008 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 21 Sayı: 6
- Basım Tarihi: 2008
- Doi Numarası: 10.1016/j.aml.2007.07.011
- Dergi Adı: Applied Mathematics Letters
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.594-598
- Anahtar Kelimeler: Countable compactness, Sequences, Sequential compactness, Series, Summability
- Maltepe Üniversitesi Adresli: Evet
Özet
A subset F of a topological space is sequentially compact if any sequence x = (xn) 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 = (xn) 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. © 2007 Elsevier Ltd. All rights reserved.