Web-compact spaces, Fréchet-Urysohn groups and a Suslin closed graph theorem
✍ Scribed by J. C. Ferrando; Jerzy Ka̧kol; M. López Pellicer; W. Śliwa
- Publisher
- John Wiley and Sons
- Year
- 2010
- Tongue
- English
- Weight
- 148 KB
- Volume
- 283
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
A topological space X is strongly web-compact if X admits a family Aα : α ∈ N N of relatively countably compact sets covering X and such that Aα ⊂ A β for α ≤ β. The main result of this paper states the following: Theorem A Let X and Y be topological groups and f a homomorphism between X and Y with closed graph. If X is Fréchet-Urysohn and Baire and Y is strongly web-compact, then f is continuous. This extends a result of Valdivia. We provide an example showing that the property of being strongly web-compact is not productive. This applies to show that there are quasi-Suslin spaces X whose product X × X is not quasi-Suslin.