More on \(P\)-closed spaces

  • Terrence A. Edwards University of the District of Columbia
  • James E. Joseph Howard University
  • Bhamini M.P. Nayar Morgan Sate University
Keywords: Ultrafilters; compactness; P-closed

Abstract

In [1] the following problems were listed as open: Problem 14. Is a regular space in which every closed subset is regular-closed compact? Problem 15. Is a Urysohn-space in which every closed subset is Urysohnclosed compact? To answer the question for Hausdorff-closed spaces in the affirmative, M. H. Stone [12] used Boolean rings and M. Katˇetov [10] used topological methods. In this article, all three questions are answered affirmatively using filters.

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Author Biographies

Terrence A. Edwards, University of the District of Columbia

Department of Mathematics

University of the District of Columbia

Washington, DC. 20008

James E. Joseph, Howard University

Retired Professor, Department of Mathematics

Howard University

Washington, DC 20059

Published
2019-11-09
How to Cite
Edwards, T. A., Joseph, J. E., & Nayar, B. M. (2019). More on \(P\)-closed spaces. Journal of Advanced Studies in Topology, 10(2), 8-10. https://doi.org/10.20454/jast.2019.1580
Section
Original Articles

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