- Tytuł:
- Compactness and countable compactness in weak topologies
- Autorzy:
- Kirk, W. A.
- Powiązania:
- https://bibliotekanauki.pl/articles/1289854.pdf
- Data publikacji:
- 1995
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
weak topologies
compactness
countable compactness
quasi-normal structure
convexity structures - Opis:
- A bounded closed convex set K in a Banach space X is said to have quasi-normal structure if each bounded closed convex subset H of K for which diam(H) > 0 contains a point u for which ∥u-x∥ < diam(H) for each x ∈ H. It is shown that if the convex sets on the unit sphere in X satisfy this condition (which is much weaker than the assumption that convex sets on the unit sphere are separable), then relative to various weak topologies, the unit ball in X is compact whenever it is countably compact.
- Źródło:
-
Studia Mathematica; 1994-1995, 112, 3; 243-250
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł