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Effros, Baire, Steinhaus and Non-Separability

Research paper by A. J. Ostaszewski

Indexed on: 14 Jun '16Published on: 14 Jun '16Published in: Mathematics - General Topology



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).