Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1983-0695276-X
MathSciNet review: 695276
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54D25, 54D18

Retrieve articles in all journals with MSC: 54D25, 54D18


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0695276-X
Keywords: Para-$ H$-closed, $ H$-closed, feebly compact, minimal-Hausdorff, pHc-closed
Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society