Domain-representable spaces

Harold Bennett¹ ; David Lutzer²

¹ Texas Tech University Lubbock, TX 79409, U.S.A.
² College of William & Mary Williamsburg, VA 23187, U.S.A.

Fundamenta Mathematicae, Tome 189 (2006) no. 3, pp. 255-268

Résumé

We study domain-representable spaces, i.e., spaces that can be represented as the space of maximal elements of some continuous directed-complete partial order (= domain) with the Scott topology. We show that the Michael and Sorgenfrey lines are of this type, as is any subspace of any space of ordinals. We show that any completely regular space is a closed subset of some domain-representable space, and that if $X$ is domain-representable, then so is any $G_\delta $-subspace of $X$. It follows that any Čech-complete space is domain-representable. These results answer several questions in the literature.

Détail

DOI : 10.4064/fm189-3-3

Keywords: study domain representable spaces spaces represented space maximal elements continuous directed complete partial order domain scott topology michael sorgenfrey lines type subspace space ordinals completely regular space closed subset domain representable space domain representable delta subspace follows ech complete space domain representable these results answer several questions literature