Faculty Publications

Title

D-spaces

Document Type

Article

Keywords

Box product, D-space, Linearly ordered topological space, Metacompact, Semistratifiable

Journal/Book/Conference Title

Topology and its Applications

Volume

114

Issue

3

First Page

261

Last Page

271

Abstract

We use U-sticky sets to show that box products of scattered spaces of height 1 are D-spaces and to simplify the proof of van Douwen and Lutzer that a subspace of a linearly ordered space is a D-space iff no closed subset is stationary. Analogously, we show that a subspace of a product of finitely many ordinals is a D-space iff it is metacompact iff no closed subset is stationary. We examine the proof that metric spaces are D-spaces and obtain a new characterization of semistratifiability. © 2001 Elsevier Science B.V. All rights reserved.

Original Publication Date

1-1-2001

DOI of published version

10.1016/s0166-8641(00)00042-0

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