Displaying similar documents to “Functions and Baire spaces”

Algebras of Borel measurable functions

Michał Morayne (1992)

Fundamenta Mathematicae

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We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.

Fine properties of Baire one functions

Udayan Darji, Michael Evans, Chris Freiling, Richard O'Malley (1998)

Fundamenta Mathematicae

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A new theorem in the theory of first return representations of Baire class one functions of a real variable is presented which has as immediate consequences several known characterizations of standard subclasses of the Baire one functions. Further, this theorem yields new insights into how finely Baire one functions can be recovered and yields a characterization of another subclass of Baire one functions.

On the density of extremal solutions of differential inclusions

F. S. De Blasi, G. Pianigiani (1992)

Annales Polonici Mathematici

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An existence theorem for the cauchy problem (*) ẋ ∈ ext F(t,x), x(t₀) = x₀, in banach spaces is proved, under assumptions which exclude compactness. Moreover, a type of density of the solution set of (*) in the solution set of ẋ ∈ f(t,x), x(t₀) = x₀, is established. The results are obtained by using an improved version of the baire category method developed in [8]-[10].

Connectivity of diagonal products of Baire one functions

Aleksander Maliszewski (1994)

Fundamenta Mathematicae

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We characterize those Baire one functions f for which the diagonal product x → (f(x), g(x)) has a connected graph whenever g is approximately continuous or is a derivative.

Structure resolvability

Rolando Jimenez, Viacheslav I. Malykhin (1998)

Commentationes Mathematicae Universitatis Carolinae

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We introduce the general notion of structure resolvability and structure irresolvability, generalizing the usual concepts of resolvability and irresolvability.