On some classes of Lindelöf Σ-spaces |
| |
Authors: | Wies?aw Kubi? Oleg Okunev Paul J. Szeptycki |
| |
Affiliation: | a Institute of Mathematics, Akademia Swietokrzyska, ul. Swietokrzyska 15, 25-406 Kielce, Poland b Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, av. San Claudio y Rio Verde s/n col. San Manuel, Ciudad Universitaria, CP 72570 Puebla, Puebla, Mexico c Mathematics, Atkinson Faculty, York University, Toronto, ON M3J 1P3, Canada |
| |
Abstract: | We consider special subclasses of the class of Lindelöf Σ-spaces obtained by imposing restrictions on the weight of the elements of compact covers that admit countable networks: A space X is in the class LΣ(?κ) if it admits a cover by compact subspaces of weight κ and a countable network for the cover. We restrict our attention to κ?ω. In the case κ=ω, the class includes the class of metrizably fibered spaces considered by Tkachuk, and the P-approximable spaces considered by Tka?enko. The case κ=1 corresponds to the spaces of countable network weight, but even the case κ=2 gives rise to a nontrivial class of spaces. The relation of known classes of compact spaces to these classes is considered. It is shown that not every Corson compact of weight ℵ1 is in the class LΣ(?ω), answering a question of Tkachuk. As well, we study whether certain compact spaces in LΣ(?ω) have dense metrizable subspaces, partially answering a question of Tka?enko. Other interesting results and examples are obtained, and we conclude the paper with a number of open questions. |
| |
Keywords: | 54D20 54A25 54C60 54F99 |
本文献已被 ScienceDirect 等数据库收录! |
|