$M$-Bornological spaces
Stanislav Tomášek · Czech digital mathematics library · 1970
Introduction, In a recent paper (cf.[8]) the class of M -barrelled spaces which represents an extension of vector spaces of the second category, has been investigated.The purpose of this article is to give such extension of metrisable topological spaces to a wider class of M -bornological spaces.It turns out that any M -bornological and locally convex space is at the same time a bornological space in the usual sense* Recall that a locally convex space E is termed bornological if any convex set B in £ absorbing an arbitrary bounded subset in E is a neighborhood of the origin in £ .As to the denotation we preserve that one used in L8].For the corresponding results and necessary notions in locally convex spaces as well as for the classical prototype of the theory of such spaces we refer to C2] f [3],C4],C5I and to [63.It should be pointed out that all vector spaces investigated in this paper are considered over the same and usual field of scalers.