Displaying similar documents to “Algebras of Borel measurable functions”

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.

On open maps of Borel sets

A. Ostrovsky (1995)

Fundamenta Mathematicae

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We answer in the affirmative [Th. 3 or Corollary 1] the question of L. V. Keldysh [5, p. 648]: can every Borel set X lying in the space of irrational numbers ℙ not G δ · F σ and of the second category in itself be mapped onto an arbitrary analytic set Y ⊂ ℙ of the second category in itself by an open map? Note that under a space of the second category in itself Keldysh understood a Baire space. The answer to the question as stated is negative if X is Baire but Y is not Baire.

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.

Strong meager properties for filters

Claude Laflamme (1995)

Fundamenta Mathematicae

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We analyze several “strong meager” properties for filters on the natural numbers between the classical Baire property and a filter being F σ . Two such properties have been studied by Talagrand and a few more combinatorial ones are investigated. In particular, we define the notion of a P⁺-filter, a generalization of the traditional concept of P-filter, and prove the existence of a non-meager P⁺-filter. Our motivation lies in understanding the structure of filters generated by complements...