The behavior of the properly of weak normality with respect to topological products is examined versus normality. The lbllowiag generalization of TamanG's theorem is proved: if X x Z~X is weakly normal then X is paracompact. Some ve~ions of Kat6tov's theorem are obtained. In particular, it is proved
Sums, products, and mappings of weakly pseudocompact spaces
β Scribed by Frederick W. Eckertson
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 591 KB
- Volume
- 72
- Category
- Article
- ISSN
- 0166-8641
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract We study the role that the axiom of choice plays in Tychonoff's product theorem restricted to countable families of compact, as well as, LindelΓΆf metric spaces, and in disjoint topological unions of countably many such spaces. (Β© 2004 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
In the present paper, we prove some Krasnosel'skii-Leray-Schauder type fixed point theorems for weak topology. Some fixed point theorems for the sum of two weakly sequentially continuous mappings are also presented. Our results extend and improve on ones from several earlier works.
We establish common fixed point theorems involving two pairs of weakly compatible mappings satisfying nonlinear contractive conditions in K -metric spaces. The presented theorems generalize, extend and improve many existing results in the literature.