Faculty Publications

Title

Unions of left-separated spaces

Document Type

Article

Journal/Book/Conference Title

Acta Mathematica Hungarica

Volume

154

Issue

1

First Page

124

Last Page

133

Abstract

A space is left-separated if it has a well ordering for which initial segments are closed. We explore when the union of two left-separated spaces must be left-separated. We prove that if X and Y are left-separated and X∪ Y is locally countable, then whenever ord ℓ(Y) ≤ ω1, X∪ Y is left-separated. In 1986, Fleissner [2] proved that if a space has a point-countable base, then it is left-separated if and only if it is σ-weakly separated. We provide a new proof of this result using elementary submodels and add an additional characterization.

Original Publication Date

2-1-2018

DOI of published version

10.1007/s10474-017-0771-x

Repository

UNI ScholarWorks, Rod Library, University of Northern Iowa

Language

en

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