Displaying similar documents to “Hyper-extensions of σ -algebras”

Spaces of measurable functions

Piotr Niemiec (2013)

Open Mathematics

Similarity:

For a metrizable space X and a finite measure space (Ω, 𝔐 , µ), the space M µ(X) of all equivalence classes (under the relation of equality almost everywhere mod µ) of 𝔐 -measurable functions from Ω to X, whose images are separable, equipped with the topology of convergence in measure, and some of its subspaces are studied. In particular, it is shown that M µ(X) is homeomorphic to a Hilbert space provided µ is (nonzero) nonatomic and X is completely metrizable and has more than one point. ...

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.