Inverse limits and mappings of minimal topological spaces

Louis M. Friedler and Dix Hayes Pettey

Vol. 71 (1977), No. 2, 429–448

DOI: 10.2140/pjm.1977.71.429

Abstract

S. W. Willard has conjectured that every H-closed space is the continuous image of a minimal Hausdorff space. In this paper we verify Willard’s conjecture and show as well that every R-closed space is the continuous image of a minimal regular space. We also identify conditions sufficient to guarantee that an H-closed space be the finite-to-one continuous image of a minimal Hausdorff space. We give an example of a nonvacuously R(ii) space whose product with itself is neither R(i) nor R(ii), and we obtain a number of results concerning inverse limits of H-closed spaces and R-closed spaces.

Mathematical Subject Classification 2000

Primary: 54D25

Milestones

Received: 22 May 1975

Revised: 24 March 1976

Published: 1 August 1977