Displaying similar documents to “Stationary reflection and the universal Baire property”

Baire spaces

R. C. Haworth, R. A McCoy

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CONTENTSIntroduction............................................................................................................ 5I. Basic properties of Baire spaces................................................................... 61. Nowhere dense sets............................................................................................... 62. First and second category sets............................................................................. 83. Baire spaces................................................................................................................

Baire-like spaces C(X,E)

Jerzy Kakol (2000)

Revista Matemática Complutense

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We characterize Baire-like spaces C(X,E) of continuous functions defined on a locally compact and Hewitt space X into a locally convex space E endowed with the compact-open topology.

Weak difference property of functions with the Baire property

Tamás Mátrai (2003)

Fundamenta Mathematicae

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We prove that the class of functions with the Baire property has the weak difference property in category sense. That is, every function for which f(x+h) - f(x) has the Baire property for every h ∈ ℝ can be written in the form f = g + H + ϕ where g has the Baire property, H is additive, and for every h ∈ ℝ we have ϕ(x+h) - ϕ (x) ≠ 0 only on a meager set. We also discuss the weak difference property of some subclasses of the class of functions with the Baire property, and the consistency...

On the preservation of Baire and weakly Baire category

Alireza Kamel Mirmostafaee, Zbigniew Piotrowski (2016)

Mathematica Bohemica

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We consider the question of preservation of Baire and weakly Baire category under images and preimages of certain kind of functions. It is known that Baire category is preserved under image of quasi-continuous feebly open surjections. In order to extend this result, we introduce a strictly larger class of quasi-continuous functions, i.e. the class of quasi-interior continuous functions. We show that Baire and weakly Baire categories are preserved under image of feebly open quasi-interior...

Ranks for baire multifunctions

Pandelis Dodos (2003)

Colloquium Mathematicae

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Various ordinal ranks for Baire-1 real-valued functions, which have been used in the literature, are adapted to provide ranks for Baire-1 multifunctions. A new rank is also introduced which, roughly speaking, gives an estimate of how far a Baire-1 multifunction is from being upper semicontinuous.