Can I read Resolutions of Topological Linear Spaces and Continuity of Linear Maps on EtoBox?

Resolutions of Topological Linear Spaces and Continuity of Linear Maps by Lech Drewnowski is a Mathematics article available to read on EtoBox.

What is Resolutions of Topological Linear Spaces and Continuity of Linear Maps about?

The main result of the paper is the following: If an F -space X is covered by a family (E α : α ∈ N N ) of sets such that E α ⊂ E β whenever α β, and f is a linear map from X to a topological linear space Y which is continuous on each of the sets E α , then f is continuous. This provides a very strong negative answer to a problem posed recently by J. Kakol and M. López Pellicer. A number of consequences of this result are given, some of which are quite curious. Also, inspired by a related question asked by J. Kakol, it is shown that if a linear map is continuous on each member of a sequence of compact sets, then it is also continuous on every compact convex set contained in the linear span of the sequence. The construction applied to prove this is then used to interpret a natural linear topology associated with the sequence as the inductive limit topology in the sense of Ph. Turpin, and thus derive its basic properties.

Who reads Resolutions of Topological Linear Spaces and Continuity of Linear Maps?

Author

Lech Drewnowski

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-247X)

Published

2007

Language

EN

Field

Mathematics (Physical Sciences)