Locally bounded linear topological spaces

FUZZY BOUNDED SETS AND TOTALLY FUZZY BOUNDED SETS IN I-TOPOLOGICAL VECTOR SPACES

In this paper, a new definition of fuzzy bounded sets and totallyfuzzy bounded sets is introduced and properties of such sets are studied. Thena relation between totally fuzzy bounded sets and N-compactness is discussed.Finally, a geometric characterization for fuzzy totally bounded sets in I- topologicalvector spaces is derived.

Some Order and Topological Properties of Locally Solid Linear Topological Riesz Spaces

A theorem of Luxemburg and Zaanen on normed Riesz spaces (Theorem 2.4 below) and one of Nakano (Theorem 2.3 below) have been extended by the author in [1] to metrizable locally solid linear topological Riesz spaces. This note gives an example which shows they cannot be further extended to nonmetrizable Hausdorff locally solid linear topological Riesz spaces. 1. Notation and basic concepts. For ...

Topological number for locally convex topological spaces with continuous semi-norms

In this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. It gives some criterions to study locally convex topological spaces in a discrete approach.

Linear Topological Spaces

The Structure of Locally Connected Topological Spaces

0.1. This paper presents an investigation of the following problem. Exhibit a class X of topological spaces which contains all peano spaces and which has the following properties: (1) a cyclic element theory exists in each space of the class, (2) the abstract set consisting of all cyclic element of any space X of the class can be topologized so as to be a member of the class X, and (3) the hype...