On 𝐻-closed and minimal Hausdorff spaces

Abstract

Introduction. Properties closely related to compactness have long been of interest to topologists. In this paper we will consider a collection of properties related to the observation that if a compact Hausdorff space X is embedded in a Hausdorff space Y, the image of X is always a closed subspace of Y. This property was first investigated by Alexandroff and Urysohn [2] in 1924, and such spaces are called H-closed. In 1940, Kattov [13] studied minimal Hausdorff spaces and observed that these are precisely the spaces which are //-closed and semiregular.