2015/10/24 by A. J. Ostaszewski · 9 citations
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #Baire category theorem #Baire measure #Baire space #Banach space #Compact space #Complete metric space #Discrete mathematics #Eberlein–Šmulian theorem #Lp space #Mathematical analysis #Mathematical and Theoretical Analysis #Mathematics #Metric space #Metrization theorem #Open mapping theorem (functional analysis) #Pure mathematics #Separable space #math.GN #msc:02K20 #msc:04A15 #msc:26A03
paper · pdf · doi:10.1016/j.topol.2015.09.033
published in Topology and its Applications 195, 265-274 (Elsevier BV) · Expanded version (including a section of commentary) of a paper for the special issue honoring the memory of Mary Ellen Rudin in Topology and its Applications
openalex publication_date 2015/10/24 · arxiv created 2016/06/14 · arxiv updated 2016/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We give a short proof of an improved version of the Effros Open Mapping Principle via a shift-compactness theorem (also with a short proof), involving `sequential analysis' rather than separability, deducing it from the Baire property in a general Baire-space setting (rather than under topological completeness). It is applicable to absolutely-analytic normed groups (which include complete metrizable topological groups), and via a Steinhaus-type Sum-set Theorem (also a consequence of the shift-compactness theorem) includes the classical Open Mapping Theorem (separable or otherwise).