Document Type

Article

Department/Program

Mathematics

Journal Title

Topology and Its Applications

Pub Date

2013

Volume

160

Issue

4

First Page

633

Abstract

In this paper we investigate generalized ordered (GO) spaces that have a flexible diagonal in the sense of Arhangel'skii (2009) [2]. Spaces with a flexible diagonal are generalizations of topological groups and include spaces that are continuously homogeneous, Choban spaces, and rotoid spaces. We prove some paracompactness and metrization theorems for such spaces and construct examples of generalized ordered spaces that clarify how the types of spaces with a flexible diagonal are interrelated. We show, for example, that any GO Choban space is hereditarily paracompact, that any continuously homogeneous, first-countable GO-space is metrizable, that the space of real numbers is the only non-degenerate connected LOTS that is a Chbban space, and that the Sorgenfrey line and the Michael line are Choban spaces. We extend some results of Arhangel'skii and pose a family of questions. (C) 2013 Elsevier B.V. All rights reserved.

DOI

10.1016/j.topol.2013.01.009

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