Universal 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 ...

On Universal Mappings and Free Topological Groups

It has been observed that constructions so apparently different as Kronecker products, extension of the ring of operators of a module, field of quotients of an integral domain, free groups, free topological groups, completion of a uniform space, Cech compactification enter in the same frame. We intend in this paper to explain a rather general process of construction which may be applied to most...

Topological Dynamics in Coset Transformation Groups

UNIVERSAL COMPACTIFICATIONS OF TRANSFORMATION SEMIGROUPS

We extend the notion of semigroup compactification to the class of transformation semigroups, and determine the compactifications which are universal with respect to some topological properties.

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...