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From B-completeness to countable codimensional subspaces via the closed graph theorem

Published online by Cambridge University Press:  14 November 2011

H. Saiflu  and
I. Tweddle
H. Saiflu
Affiliation:
Department of Mathematics, University of Tabriz, Iran
I. Tweddle
Affiliation:
Department of Mathematics, University of Stirling
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Synopsis

We show that for some closed graph theorems each countable codimensional subspace of a domain space may also serve as a domain space. This provides a general principle from which we are able to extract some of the known results on the inheritance of topological vector space properties by subspaces of countable codimension. We make use of a result of Savgulidze and Smoljanov on B-completeness for which we provide a new and simpler proof.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 86 , Issue 1-2 , 1980 , pp. 107 - 114
Copyright
Copyright © Royal Society of Edinburgh 1980

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