On minimal Hausdorff frames
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DOI:
https://doi.org/10.26637/MJM0804/0046Abstract
The concept of minimal Hausdorff topological spaces was studied and characterized by M.P. Berri. A compact Hausdorff space is minimal Hausdorff and such spaces are reversible in the sense that every continuous self bijection is a homeomorphism. In this paper we study minimal Hausdorffness in the context of pointfree topology. We introduce the notion of minimal Hausdorff frames and characterize them in terms of convergence of filters in frames. We also study the association between minimal Hausdorff frames and minimal Hausdorff topological spaces. An application is to prove that a minimal Hausdorff frame is a reversible frame in the sense that every order preserving self bijection is a frame isomorphism.
Keywords:
Frame, minimal Hausdorff frame, subframe, sublocale, filter, clustered filter.Mathematics Subject Classification:
General Mathematics- Pages: 1597-1602
- Date Published: 01-10-2020
- Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)
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