If Martin’s Axiom is true and the continuum hypothesis is false, and X is a compact Radon measure space with a non-separable space, then there is a continuous surjection from X onto .
I discuss the properties of α-favourable and weakly α-favourable measure spaces, with remarks on their relations with other classes.
We investigate the products of topological measure spaces, discussing conditions under which all open sets will be measurable for the simple completed product measure, and under which the product of completion regular measures will be completion regular. In passing, we describe a new class of spaces on which all completion regular Borel probability measures are τ-additive, and which have other interesting properties.
We introduce the notions of Kuratowski-Ulam pairs of topological spaces and universally Kuratowski-Ulam space. A pair (X,Y) of topological spaces is called a Kuratowski-Ulam pair if the Kuratowski-Ulam Theorem holds in X× Y. A space Y is called a universally Kuratowski-Ulam (uK-U) space if (X,Y) is a Kuratowski-Ulam pair for every space X. Obviously, every meager in itself space is uK-U. Moreover, it is known that every space with a countable π-basis is uK-U. We prove the following: ...
I discuss the number of iterations of the elementary sequential closure operation required to achieve the full sequential closure of a set in spaces of the form .
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