Domain-representable spaces

• Autorzy: Harold Bennett , David Lutzer
• Języki publikacji: EN

Abstrakty

EN

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 $G_{δ}$-subspace of X. It follows that any Čech-complete space is domain-representable. These results answer several questions in the literature.

Kategorie tematyczne

• 06B35: Continuous lattices and posets, applications
• 54E52: Baire category, Baire spaces
• 06F30: Topological lattices, order topologies
• 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2006
• Tom: 189
• Numer: 3
• Strony: 255-268

Daty

wydano

2006

Twórcy

autor

Harold Bennett

• Texas Tech University, Lubbock, TX 79409, U.S.A.

autor

David Lutzer

• College of William & Mary, Williamsburg, VA 23187, U.S.A.

Identyfikatory

DOI

10.4064/fm189-3-3