How a Change to Topology's Union Axiom Affects Continuity
General Topology
2022-01-27 v1
Abstract
The most general definition of a continuous function requires that the preimage of any open set be open. Thus, to discuss continuity in the abstract, it is necessary to first define a topology, which tells us which sets in a space are open. Such a topology is given by three axioms that describe how the open sets in a topology behave. In this paper we shall consider a change to one of these axioms and determine how this change affects the continuity of a function.
Cite
@article{arxiv.2201.10977,
title = {How a Change to Topology's Union Axiom Affects Continuity},
author = {Rachel Bergjord and Matthew Zabka},
journal= {arXiv preprint arXiv:2201.10977},
year = {2022}
}
Comments
6 pages, submitted to Axioms