Displaying similar documents to “An abstract version of Sierpiński's theorem and the algebra generated by A and CA functions”

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.

Uniformly completely Ramsey sets

Udayan Darji (1993)

Colloquium Mathematicae

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Galvin and Prikry defined completely Ramsey sets and showed that the class of completely Ramsey sets forms a σ-algebra containing open sets. However, they used two definitions of completely Ramsey. We show that they are not equivalent as they remarked. One of these definitions is a more uniform property than the other. We call it the uniformly completely Ramsey property. We show that some of the results of Ellentuck, Silver, Brown and Aniszczyk concerning completely Ramsey sets also...

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.

A contribution to the topological classification of the spaces Ср(X)

Robert Cauty, Tadeusz Dobrowolski, Witold Marciszewski (1993)

Fundamenta Mathematicae

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We prove that for each countably infinite, regular space X such that C p ( X ) is a Z σ -space, the topology of C p ( X ) is determined by the class F 0 ( C p ( X ) ) of spaces embeddable onto closed subsets of C p ( X ) . We show that C p ( X ) , whenever Borel, is of an exact multiplicative class; it is homeomorphic to the absorbing set Ω α for the multiplicative Borel class M α if F 0 ( C p ( X ) ) = M α . For each ordinal α ≥ 2, we provide an example X α such that C p ( X α ) is homeomorphic to Ω α .

Semiring of Sets: Examples

Roland Coghetto (2014)

Formalized Mathematics

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This article proposes the formalization of some examples of semiring of sets proposed by Goguadze [8] and Schmets [13].

Weak variants of Martin's Axiom

J. Barnett (1992)

Fundamenta Mathematicae

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Examples exist of smooth maps on the boundary of a smooth manifold M which allow continuous extensions over M without fixed points but no such smooth extensions. Such maps are studied here in more detail. They have a minimal fixed point set when all transversally fixed maps in their homotopy class are considered. Therefore we introduce a Nielsen fixed point theory for transversally fixed maps on smooth manifolds without or with boundary, and use it to calculate the minimum number of...