## Abstract A Fréchet space __E__ is quasi‐reflexive if, either dim(__E__″/__E__) < ∞, or __E__″[__β__(__E__″,__E__′)]/__E__ is isomorphic to __ω__. A Fréchet space __E__ is totally quasi‐reflexive if every separated quotient is quasi‐reflexive. In this paper we show, using Schauder bases, that __E
Separation properties in neighbourhood and quasi-apartness spaces
✍ Scribed by Robin Havea; Hajime Ishihara; Luminiţa Vîţă
- Publisher
- John Wiley and Sons
- Year
- 2008
- Tongue
- English
- Weight
- 97 KB
- Volume
- 54
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
We investigate separation properties for neighbourhood spaces in some details within a framework of constructive mathematics, and define corresponding separation properties for quasi‐apartness spaces. We also deal with separation properties for spaces with inequality. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
📜 SIMILAR VOLUMES
We study separation properties of non-Tychonoff spaces that are different from the well-known separation axioms and will play important roles in the theory of general topological spaces. Then, the notions of countably w-paracompact spaces and w-metrizable spaces are introduced, which are closely rel
A subset X of a vector space V is said to have the "Separation Property" if it separates linear forms in the following sense: given a pair (α, β) of linearly independent linear forms on V there is a point x on X such that α(x) = 0 and β(x) = 0. A more geometric way to express this is the following:
## Abstract Regular left __K__‐sequentially complete quasi‐metric spaces are characterized. We deduce that these spaces are complete Aronszajn and that every metrizable space admitting a left __K__‐sequentially complete quasi‐metric is completely metrizable. We also characterize quasi‐metric spaces