An Extension of the Baire Property

Christopher Caruvana; Robert R. Kallman

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arXiv · 1703.08879

An Extension of the Baire Property

Christopher Caruvana·Robert R. Kallman

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Abstract

The purpose of this paper is to define for every Polish space $X$ a class of sets, the $EBP(X)$-sets or the extended Baire property sets, to work out many properties of the $EBP(X)$-sets and to show their usefulness in analysis. For example, a proper generalization of the Pettis Theorem is proved in this context that furnishes a new automatic continuity result for Polish groups. The name extended Baire property sets is reasonable since $EBP(X)$ contains the Baire property sets $BP(X)$ and it is consistent with ZFC that the containment is proper.

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BibTeX RIS

Christopher Caruvana, Robert R. Kallman. 2017-03-26. An Extension of the Baire Property. https://arxiv.org/abs/1703.08879

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