Title
Clopen Objects, Connected Objects, and Normalized Topological Categories
Document Type
Article
Publication Date
2021
Abstract
In this paper we extend the notion of a clopen subset of a topological space to that of a clopen subobject in a topological category. We relate clopen subobjects to the concept of normalized topological category via a theorem which, in turn, shows why certain subsets must be clopen in a topological space. We employ clopen subobjects to extend the topological notion of connectedness to topological categories. Examples of clopen subobjects and connected objects in several topological categories are given.
DOI
https://doi.org/10.1016/j.topol.2021.107593
Recommended Citation
Stine, J. (2021). Clopen objects, connected objects, and normalized topological categories. Topology and Its Applications, 290. https://doi.org/10.1016/j.topol.2021.107593