A generalized inductive limit topology for linear spaces

Inductive limit topologies on Orlicz spaces

Let L be an Orlicz space defined by a convex Orlicz function φ and let E be the space of finite elements in L (= the ideal of all elements of order continuous norm). We show that the usual norm topology Tφ on L restricted to E can be obtained as an inductive limit topology with respect to some family of other Orlicz spaces. As an application we obtain a characterization of continuity of linear ...

Admissible domain representations of inductive limit spaces

In this paper we consider the following separate but related questions: “How do we construct an effective admissible domain representation of a space X from a pseudobasis on X?”, and “How do we construct an effective admissible domain representation of the inductive limit of a directed system (Xi)i∈I of topological spaces, given effective admissible domain representations of the individual spac...

Hyperbolic topology of normed linear spaces

In a previous paper [6], the authors introduced the hyperbolic topology on a metric space, which is weaker than the metric topology and naturally derived from the Lawson topology on the space of formal balls. In this paper, we characterize spaces Lp(Ω,Σ, μ) on which the hyperbolic topology induced by the norm ∥·∥p coincides with the norm topology. We show the following. (1) The hyperbolic topol...

Dual Generalized Bases in Linear Topological Spaces

Some Generalizations on Generalized Topology and Minimal Structure Spaces

The aim of this paper is to introduce some generalizations for closed sets in generalized topology and minimal structure spaces. We investigate some properties of these sets on these spaces. Moreover, we give the concept of T0-GTMS spaces, T1/2-GTMS spaces and R0-GTMS spaces, and the various relationships between them.