Affiliation:
1. Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia
2. Department of Mathematics, Women Section, King Saud University, Riyadh, Saudi Arabia
Abstract
Starting with a category SL-CONVGRP, of stratified enriched
cl-premonoid-valued convergence groups as introduced earlier, we present a
category SL-CONVTGRP, of stratified enriched cl-premonoid-valued convergence
transformation groups, the idea behind this category is crept in the notion
of convergence transformation group - a generalization of topological
transformation group. In this respect, we are able to provide natural
examples in support to our endeavor; these examples, however, stem from the
action of convergence approach groups on convergence approach spaces, and
the action of probabilistic convergence groups under triangular norm on
probabilistic convergence spaces. Based on the category of enriched
lattice-valued convergence spaces, a Cartesian closed category that enjoys
lattice-valued convergence structure on function space, we look into among
others, the lattice-valued convergence structures on the group of
homeomorphisms of enriched lattice-valued convergence spaces, generalizing a
concept of convergence transformation groups on convergence spaces,
obtaining a characterization.
Publisher
National Library of Serbia
Cited by
1 articles.
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