Fuzzy Topological Transformation Groups

Topological Transformation Groups

1. Introduction This note will summarize some of the recent work on topological groups and discuss a few topics in transformation groups mainly in S 3 and S 4. In one aspect of this subject, namely the relation of general locally compact groups to Lie groups, information is now fairly complete. However in most other aspects the situation is far less satisfactory and in many areas known results ...

Strong Fuzzy Topological Groups

Following the introduction of fuzzy sets in 1965, a notion of fuzzy topological group was proposed by Foster in 1979: essentially he took a group and furnished it with a fuzzy topological structure. An equivalent notion of fuzzy topological group was introduced by Ma and Yu in 1984 by replacing points by fuzzy points. Recently two of the coauthors have introduced the notion of the topology indu...

Topological Dynamics in Coset Transformation 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.