The Theory of S-Spaces
Taqdir Husain · 1965
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. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.