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
On hereditary normality of zero-dimensional spaces
β Scribed by Sergei Logunov
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 67 KB
- Volume
- 102
- 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 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.
π SIMILAR VOLUMES
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.
Assuming the continuum hypothesis we give an example of a completely regular space F without any dense finite-dimensional subspace whose square Fx F contains a dense zero-dimensional subspace; the construction is based on an example of a metrizable separable space H whose all uncountable subsets are