We show that there are two (isomorphic) full subcategories of the category of locally convex topological vector spaces—the weakly topologized spaces and those with the Mackey topology—that form ∗-autonomous categories. RÉSUMÉ. On montre qu’il y a deux sous-catégories (isomorphes) pleines de la catégorie des espaces vectoriels topologiques localement convexes—les espaces munis de la topologie fa...

In this paper the concept of S-neighborhoods is introduced and we give a new characterization of L-topological vector spaces in terms of S-neighborhood base of θλ(λ ∈ M(L)). As an application, we obtain a necessary and sufficient condition of a vector Ltopology determined by its level topologies. Copyright c ©2003 Yang’s Scientific Research Institute, LLC. All rights reserved.

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

In this paper we study hereditarily homogeneous generalized topological spaces. Various properties of hereditarily homogeneous generalized topological spaces are discussed. We prove that a generalized topological space is hereditarily homogeneous if and only if every transposition of $X$ is a $mu$-homeomorphism on $X$.

and Applied Analysis 3 It follows from 2.1 and 2.6 that 2f ( x y 2 ) − g x − h(y) 2f ( x y 2 ) − g(y z) − h x − z − [ 2f (x z 2 ) − g 2z − h x − z ] [ 2f ( y 2z 2 ) − g 2z − h(y) ] − [ 2f ( y 2z 2 ) − g(y z) − h z ] [ 2f (x z 2 ) − g x − h z ] ∈ 3V − 2V 2.7 for all x, y ∈ X with ‖x‖ ‖y‖ < d. Hence, by 2.1 and 2.7 , we have 2f ( x y 2 ) − g x − h(y) ∈ 3V − 2V 2.8 for all x, y ∈ X. Letting x 0 y ...