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Minimal topologies of para-$ H$-closed spaces

Author: Muhammad I. Zahid
Journal: Proc. Amer. Math. Soc. 88 (1983), 363-366
MSC: Primary 54D25; Secondary 54D18
MathSciNet review: 695276
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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 [Enhancements On Off] (What's this?)

  • [1] M. P. Berri, Minimal topological spaces, Trans. Amer. Math. Soc. 108 (1963), 97-105. MR 0150724 (27:711)
  • [2] C. S. Scarborough and R. M. Stephenson, Jr., Minimal topologies, Colloq. Math. 19 (1968), 215-219. MR 0227938 (37:3522)
  • [3] M. I. Zahid, Para-$ H$-closed spaces, locally para-$ H$-closed spaces and their minimal topologies, Ph.D. Dissertation, University of Pittsburgh, 1981.

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Keywords: Para-$ H$-closed, $ H$-closed, feebly compact, minimal-Hausdorff, pHc-closed
Article copyright: © Copyright 1983 American Mathematical Society

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