Minimal topologies of para-$H$-closed spaces
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- by Muhammad I. Zahid PDF
- Proc. Amer. Math. Soc. 88 (1983), 363-366 Request permission
Abstract:
A Hausdorff space is para-$H$-closed if every open cover has a locally-finite open refinement (not necessarily covering the space) whose union is dense in the space. We prove that minimal locally-$H$-closed, minimal locally-para-$H$-closed and minimal para-$H$-closed spaces are all minimal-Hausdorff. We also show that para-$H$-closed-closed spaces are $H$-closed.References
- Manuel P. Berri, Minimal topological spaces, Trans. Amer. Math. Soc. 108 (1963), 97–105. MR 150724, DOI 10.1090/S0002-9947-1963-0150724-0
- C. T. Scarborough and R. M. Stephenson, Minimal topologies, Colloq. Math. 19 (1968), 215–219. MR 227938, DOI 10.4064/cm-19-2-215-219 M. I. Zahid, Para-$H$-closed spaces, locally para-$H$-closed spaces and their minimal topologies, Ph.D. Dissertation, University of Pittsburgh, 1981.
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 88 (1983), 363-366
- MSC: Primary 54D25; Secondary 54D18
- DOI: https://doi.org/10.1090/S0002-9939-1983-0695276-X
- MathSciNet review: 695276