It is proved that if all Fg-sets in the product X x Y are &normal, then either X is normal and countably paracompact or all countable subsets of Y are closed. If the product X x Y is hereditarily S-normal, then either X is perfectly normal or all countable subsets of Y are closed. Applications to ex
On hereditary normality of compactifications
β Scribed by Sergej Logunov
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 241 KB
- Volume
- 73
- Category
- Article
- ISSN
- 0166-8641
No coin nor oath required. For personal study only.
β¦ Synopsis
We show, in particular, that if X is a locally compact second countable space without isolated points, then each point of the remainder of the space /?X is a nonnormality point of PX.
π SIMILAR VOLUMES
In 1964 K. Morita introduced the concept of P(m)-spaces which characterized the normality of products with any metrizable space of weight < m. Especially, a topological space X is a normal P(No)-space if and only if X x Y is normal for any separable metrizable space Y. Okuyama (1991) introduced a si
We show, in particular, that if X is a zero-dimensional second countable space without isolated points, then each point of the remainder of the space Ξ²X is a non-normality point of Ξ²X.
Let (X, Y ) be a minimal compactifiurtion of C 2 . In this paper, we determine the structure of such a (X,Y) in the case where X is a normal hypersurface of degree d 5 4 i n P3. ## 1. Introduction A projective normal Gorenstein surface X over C is called a compactification of C if there is a clo