A base B for a topological space X is said to be sharp if for every x β X and every sequence (U n ) nβΟ of pairwise distinct elements of B with x β U n for all n the set { i<n U i : n β Ο} forms a base at x. Sharp bases of T 0 -spaces are weakly uniform. We investigate which spaces with sharp bases
Weakly uniform bases and the first countability axiom
β Scribed by S. A. Peregudov
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 1986
- Tongue
- English
- Weight
- 505 KB
- Volume
- 40
- Category
- Article
- ISSN
- 0001-4346
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract Two theorems are proved: First that the statement βthere exists a field __F__ such that for every vector space over __F__, every generating set contains a basisβ implies the axiom of choice. This generalizes theorems of Halpern, Blass, and Keremedis. Secondly, we prove that the assert
## Abstract We show that the both assertions βin every vector space __B__ over a finite element field every subspace __V__ β __B__ has a complementary subspace __S__β and βfor every family π of disjoint odd sized sets there exists a subfamily β±={F~j~:j Ο΅Ο} with a choice functionβ together imply the