Effros, Baire, Steinhaus and Non-Separability
General Topology
2016-06-15 v1
Abstract
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).
Cite
@article{arxiv.1606.04496,
title = {Effros, Baire, Steinhaus and Non-Separability},
author = {A. J. Ostaszewski},
journal= {arXiv preprint arXiv:1606.04496},
year = {2016}
}
Comments
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