The Theory of S-Spaces

Taqdir Husain
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Taqdir Husain: McMaster University

Chapter 6 in The Open Mapping and Closed Graph Theorems in Topological Vector Spaces, 1965, pp 71-81 from Springer

Abstract: Abstract The theory of S-spaces is due to T. Husain [14]. Some of the important properties of S-spaces are the following: (a) they are not necessarily metrizable, although every metrizable 1.c. space is an S-space; (b) the Krein—Šmulian theorem which is true for Fréchet spaces can also be proved for complete S-spaces; (c)the completion of an S-space is B-complete; (d) every subspace of an S-space E is an S-space provided E satisfies a closure property (see the main text); (e) the dual E′c of a complete S-space E is B r -complete, provided E satisfies the closure property.

Keywords: Open Mapping; Open Neighbourhood; Finite Subset; Closure Property; Dense Subspace (search for similar items in EconPapers)
Date: 1965
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DOI: 10.1007/978-3-322-96210-2_6

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