Covering Maps with respect to Topologies on the Fundamental Group
Naghme Shahami, Behrooz Mashayekhy

TL;DR
This paper generalizes classical covering maps by introducing a new concept of ^{ au}-covering maps, which unify various types of coverings through topologies on the fundamental group, and compares their properties.
Contribution
It introduces a new generalized covering map concept ^{ au}-covering, unifying classical, semi, generalized coverings, and fibrations under a topological framework on the fundamental group.
Findings
^{ au}-covering maps encompass classical and generalized coverings.
Comparison of ^{ au}-coverings for different topologies on (X).
Properties of ^{ au}-coverings are established and analyzed.
Abstract
In this paper, using the classical covering theory, we introduce a generalization of covering maps of a space with respect to a topology on the fundamental group of . We show that the famous notions, covering, semicovering, generalized covering and fibration maps are of special cases of this new notion -covering map. Moreover, among presenting some properties for this new notion, we compare -covering maps of a space for several famous topologies on the fundamental group of .
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Fuzzy and Soft Set Theory · Rings, Modules, and Algebras
