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How a Change to Topology's Union Axiom Affects Continuity

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arxiv 2201.10977 v1 pith:FOT6OMU6 submitted 2022-01-26 math.GN

Rachel Bergjord , Matthew Zabka This is my paper · ORCID
classification math.GN
keywords opentopologychangecontinuityaffectsaxiomsfunctionsets
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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.

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