6533b7cffe1ef96bd12582b6
RESEARCH PRODUCT
On Słowikowski, Raíkov and De Wilde Closed Graph Theorems
M. Valdiviasubject
Topological manifoldDiscrete mathematicsPure mathematicsConnected spaceClosed setDense setLocally convex topological vector spaceClosed graph theoremTopological spaceTopological vector spaceMathematicsdescription
Publisher Summary This chapter focuses on the Slowikowski, Raikov and De Wilde closed graph theorems. The vector spaces used in the chapter, are defined over the field Ղ of real or complex numbers. The term, “space” means separated topological vector space, unless the contrary is specifically stated. If Ω is a non-empty open subset of the n -dimensional euclidean space, then the Schwartz space ҟ′(Ω) endowed with the strong topology belongs to this class. The chapter also studies the classes of spaces related with this conjecture. The class of Slowikowski spaces contains the F-spaces and it is stable with respect to the operations that include: countable topological direct sums, closed subspaces, countable topological products, and continuous linear images.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1986-01-01 |