Displaying similar documents to “ c -Luzin sets, nonatomic σ -fields and σ -independent sets”

Is the product of ccc spaces a ccc space?

Nina M. Roy (1989)

Publicacions Matemàtiques

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In this expository paper it is shown that Martin's Axiom and the negation of the Continuum Hypothesis imply that the product of ccc spaces is a ccc space. The Continuum Hypothesis is then used to construct the Laver-Gavin example of two ccc spaces whose product is not a ccc space.

When ℵ₁ many sets are contained in a countably generated σ-field

R. Drabiński, E. Grzegorek (2009)

Colloquium Mathematicae

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We discuss the problem when ℵ₁ sets are contained in a σ-generated σ-field on some set X. This is related to a problem raised by K. P. S. Bhaskara Rao and Rae Michael Shortt [Dissertationes Math. 372 (1998)] which we answer. We also briefly discuss generating the family of all subsets from rectangles.

An uncountable partition contained in the atomless σ-field

Radosław Drabiński (2011)

Colloquium Mathematicae

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This short note considers the question of whether every atomless σ-field contains an uncountable partition. The paper comments the situation for a couple of known σ-fields. A negative answer to the question is the main result.