Displaying similar documents to “On the equivalence between CH and the existence of certain ℐ -Luzin subsets of ℝ .”

Generalized projections of Borel and analytic sets

Marek Balcerzak (1996)

Colloquium Mathematicae

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For a σ-ideal I of sets in a Polish space X and for A ⊆ X 2 , we consider the generalized projection (A) of A given by (A) = x ∈ X: Ax ∉ I, where A x =y ∈ X: 〈x,y〉∈ A. We study the behaviour of with respect to Borel and analytic sets in the case when I is a ∑ 2 0 -supported σ-ideal. In particular, we give an alternative proof of the recent result of Kechris showing that [ ∑ 1 1 ( X 2 ) ] = ∑ 1 1 ( X ) for a wide class of ∑ 2 0 -supported σ-ideals.

Very small sets

Haim Judah, Amiran Lior, Ireneusz Recław (1997)

Colloquium Mathematicae

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On the maximal spectrum of commutative semiprimitive rings

K. Samei (2000)

Colloquium Mathematicae

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The space of maximal ideals is studied on semiprimitive rings and reduced rings, and the relation between topological properties of Max(R) and algebric properties of the ring R are investigated. The socle of semiprimitive rings is characterized homologically, and it is shown that the socle is a direct sum of its localizations with respect to isolated maximal ideals. We observe that the Goldie dimension of a semiprimitive ring R is equal to the Suslin number of Max(R).

A Classical Olivier’s Theorem and Statistical Convergence

Tibor Šalát, Vladimír Toma (2003)

Annales mathématiques Blaise Pascal

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L. Olivier proved in 1827 the classical result about the speed of convergence to zero of the terms of a convergent series with positive and decreasing terms. We prove that this result remains true if we omit the monotonicity of the terms of the series when the limit operation is replaced by the statistical limit, or some generalizations of this concept.