Displaying similar documents to “Measurable spaces with c.c.c.”

When is ℝ the union of an increasing family of null sets?

Juan González-Hernández, Fernando Hernández-Hernández, César E. Villarreal (2007)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We study the problem in the title and show that it is equivalent to the fact that every set of reals is an increasing union of measurable sets. We also show the relationship of it with Sierpi'nski sets.

Characterization of realcompactness and hereditary realcompactness in the class of normal nodec (submaximal) spaces

Mehrdad Karavan (2016)

Colloquium Mathematicae

Similarity:

Is it true in ZFC that every normal submaximal space of non-measurable cardinality is hereditarily realcompact? This question (posed by O. T. Alas et al. (2002)) is given a complete affirmative answer, for a wider class of spaces. In fact, this answer is a part of a bi-conditional statement: A normal nodec space X is hereditarily realcompact if and only if it is realcompact if and only if every closed discrete (or nowhere dense) subset of X has non-measurable cardinality.