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Remarks on bounded sets in ( L F ) t v -spaces

Jerzy Kąkol (1995)

Commentationes Mathematicae Universitatis Carolinae

We establish the relationship between regularity of a Hausdorff ( L B ) t v -space and its properties like (K), M.c.c., sequential completeness, local completeness. We give a sufficient and necessary condition for a Hausdorff ( L B ) t v -space to be an ( L S ) t v -space. A factorization theorem for ( L N ) t v -spaces with property (K) is also obtained.

Sequential retractivities and regularity on inductive limits

Qiu Jing-Hui (2000)

Czechoslovak Mathematical Journal

In this paper we prove the following result: an inductive limit ( E , t ) = ind ( E n , t n ) is regular if and only if for each Mackey null sequence ( x k ) in ( E , t ) there exists n = n ( x k ) such that ( x k ) is contained and bounded in ( E n , t n ) . From this we obtain a number of equivalent descriptions of regularity.

Sequentially complete inductive limits and regularity

Claudia Gomez-Wulschner, Jan Kučera (2004)

Czechoslovak Mathematical Journal

A notion of an almost regular inductive limits is introduced. Every sequentially complete inductive limit of arbitrary locally convex spaces is almost regular.

Some aspects of the modern theory of Fréchet spaces.

Klaus D. Bierstedt, José Bonet (2003)

RACSAM

We survey some recent developments in the theory of Fréchet spaces and of their duals. Among other things, Section 4 contains new, direct proofs of properties of, and results on, Fréchet spaces with the density condition, and Section 5 gives an account of the modern theory of general Köthe echelon and co-echelon spaces. The final section is devoted to the developments in tensor products of Fréchet spaces since the negative solution of Grothendieck?s ?problème des topologies?.

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