Unions of left-separated spaces
Acta Mathematica Hungarica
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  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
DOI of published version
UNI ScholarWorks, Rod Library, University of Northern Iowa
Scheidecker, E. and Stanley, A., "Unions of left-separated spaces" (2018). Faculty Publications. 749.