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A characterization of maximal regular ideals in lmc algebras

100%

Fragoulopoulou M.

Studia Mathematica

1992

tom 103

nr 1

41-49

A question of Warner and Whitley concerning a nonunital version of the Gleason-Kahane-Żelazko theorem is considered in the context of nonnormed topological algebras. Among other things it is shown that a closed hyperplane M of a commutative symmetric F*-algebra E with Lindelöf Gel'fand space is a maximal regular ideal iff each element of M belongs to some closed maximal regular ideal of E.

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A covering criterion and its applications to product theorems

100%

Jachymski J.

Commentationes Mathematicae

2005

tom 45

nr 1

We establish a covering criterion involving a neighbourhood system and ideals of open sets which yields, in particular, a compactness criterion for an arbitrary topological space. As an application, we give new proofs of Tychonoff’s compactness theorem: we consider separately the case of a countable product, in a proof of which the ordinary mathematical induction is used, and the case of an uncountable product proved by the transfinite induction. Subsequently, the same argument is applied to obtain some results on products of Lindelöf spaces.

Ograniczanie wyników

1 Commentationes Mathematicae

1 Studia Mathematica

1 Fragoulopoulou M.

1 Jachymski J.

1 2005

1 1992

Wyniki wyszukiwania

A characterization of maximal regular ideals in lmc algebras

A covering criterion and its applications to product theorems