Topological AE (0)-groups

L-FUZZIFYING TOPOLOGICAL GROUPS

The main purpose of this paper is to introduce a concept of$L$-fuzzifying topological groups (here $L$ is a completelydistributive lattice) and discuss some of their basic properties andthe structures. We prove that its corresponding $L$-fuzzifyingneighborhood structure is translation invariant. A characterizationof such topological groups in terms of the corresponding$L$-fuzzifying neighborhoo...

PRECOMPACT TOPOLOGICAL GENERALIZED GROUPS

In this paper, we introduce and study the notion of precompacttopological generalized groups and some new results are given.

Range - preserving AE ( 0 ) - spaces

All spaces here are Tychonoff spaces. The class AE(0) consists of those spaces which are absolute extensors for compact zero-dimensional spaces. We define and study here the subclass AE(0), consisting of those spaces for which extensions of continuous functions can be chosen to have the same range. We prove these results. If each point of T ∈ AE(0) is a Gδ-point of T , then T ∈ AE(0) . These ar...

A note on quasi irresolute topological groups

In this study, we investigate the further properties of quasi irresolute topological groups defined in [20]. We show that if a group homomorphism f between quasi irresolute topological groups is irresolute at $e_G$, then $f$ is irresolute on $G$. Later we prove that in a semi-connected quasi irresolute topological group $(G,*,tau )$, if $V$ is any symmetric semi-open neighborhood of $e_G$, then...

S ep 2 00 0 COVERING GROUPS OF NON - CONNECTED TOPOLOGICAL GROUPS REVISITED