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The conjugate of a product of linear relations

Jacob J. Jaftha — 2006

Commentationes Mathematicae Universitatis Carolinae

Let X , Y and Z be normed linear spaces with T ( X → Y ) and S ( Y → Z ) linear relations, i.e. setvalued maps. We seek necessary and sufficient conditions that would ensure that ( S T ) ' = T ' S ' . First, we cast the concepts of relative boundedness and co-continuity in the set valued case and establish a duality. This duality turns out to be similar to the one that exists for densely defined linear operators and is then used to establish the necessary and sufficient conditions. These conditions are similar to those for the single...

On the completeness of localic groups

Bernhard Banaschewski;  Jacob J. C Vermeulen — 1999

Commentationes Mathematicae Universitatis Carolinae

The main purpose of this paper is to show that any localic group is complete in its two-sided uniformity, settling a problem open since work began in this area a decade ago. In addition, a number of other results are established, providing in particular a new functor from topological to localic groups and an alternative characterization of L T -groups.

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