Web‐compact spaces,Fréchet‐Urysohn groups and a Suslin closed graph theorem |
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| Authors: | J C Ferrando Jerzy Ka?kol M López Pellicer W ?liwa |
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| Institution: | 1. Centro de Investigación Operativa, Universidad Miguel Hernández, E‐03202 Elche Alicante, Spain;2. Phone: +34966658712, Fax: +34966658715;3. Faculty of Mathematics and Informatics, A. Mickiewicz University, 61‐614 Poznań, Poland;4. Depto. de Matemática Aplicada and IMPA, Universidad Politécnica de Valencia, E‐46022 Valencia, Spain;5. Phone: +34963877716, Fax: +3496387139;6. Phone: +48(0)61 8295365, Fax: +48(0)61 8295315 |
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| Abstract: | A topological space X is strongly web‐compact if X admits a family {Aα: α ∈ ??} of relatively countably compact sets covering X and such that Aα ? Aβ 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 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Web‐compact space quasi‐Suslin space K ‐analytic space analytic space Fré chet‐Urysohn space topological group |
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