Notes from a 1994–95 graduate course. Designed to supplement the topological vector space chapters of Rudin's Functional Analysis.

We give in this paper conditions for a mapping to be globally injective in a topological vector space.

A connection between the separability and the countable chain condition of spaces with L-property (a topological space X has L-property if for every topological space Y , separately continuous function f : X ×Y →R and open set I ⊆R, the set f −1(I) is an Fσ-set) is studied. We show that every completely regular Baire space with the L-property and the countable chain condition is separable and c...

in this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  we relate the cohomology of a normal subgroup $n$ of a topological group $g$ and the quotient $g/n$ to the cohomology of $g$. we get the inflation-restriction exact sequence. also, we obtain a seven-term exact cohomology sequence up to dimension 2. we give an interpretation of the first non-a...

we introduce some new concepts of topological spaces which say α − separable topologicalspace and o-topological group, α − first axiom, α − second axiom, and we find some relations betweenthem with some applications in normed spaces.

This paper de1nes the new concept of completely Hausdor& axiom of an L-topological space by means of L-continuous mappings from an L-topological space to the re1ned Hutton’s unit L-interval by Wang. Some characterizations of the completely Hausdor& axiom, de1ned in this paper, are given, and many nice properties of this kind of completely Hausdor& axiom are proved. For example, it is hereditary...