Separated and prime compactifications
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Date
2022
Authors
Journal Title
Journal ISSN
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Publisher
Elsevier BV
Abstract
We discuss conditions under which certain compactifications of topological spaces can be obtained by composing the ultrafilter space monad with suitable reflectors. In particular, we show that these compactifications inherit their categorical properties from the ultrafilter space monad. We further observe that various constructions such as the prime open filter monad defined by H. Simmons, the prime closed filter compactification studied by Bentley and Herrlich, as well as the separated completion monad studied by Salbany fall within the same categorical framework.
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Keywords
Compactification, Monad, Eilenberg-Moore algebras, Reflective subcategories
Citation
Razafindrakoto, A. (2022). Separated and prime compactifications. Topology And Its Applications, 309, 107911. doi: 10.1016/j.topol.2021.107911