Displaying similar documents to “Baire classes of affine vector-valued functions”

Remark on the Abstract Dirichlet Problem for Baire-One Functions

Ondřej F. K. Kalenda (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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We study the possibility of extending any bounded Baire-one function on the set of extreme points of a compact convex set to an affine Baire-one function and related questions. We give complete solutions to these questions within a class of Choquet simplices introduced by P. J. Stacey (1979). In particular we get an example of a Choquet simplex such that its set of extreme points is not Borel but any bounded Baire-one function on the set of extreme points can be extended to an affine...

Affine Baire functions on Choquet simplices

Miroslav Kačena, Jiří Spurný (2011)

Open Mathematics

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We construct a metrizable simplex X such that for each n ɛ ℕ there exists a bounded function f on ext X of Baire class n that cannot be extended to a strongly affine function of Baire class n. We show that such an example cannot be constructed via the space of harmonic functions.

The Dirichlet problem for Baire-one functions

Jiří Spurný (2004)

Open Mathematics

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Let X be a compact convex set and let ext X stand for the set of all extreme points of X. We characterize those bounded function defined on ext X which can be extended to an affine Baire-one function on the whole set X.

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................................................................................................................

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.

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.