Some observations on filters with properties defined by open covers
We study the relation between the Hurewicz and Menger properties of filters considered topologically as subspaces of with the Cantor set topology.
We study the relation between the Hurewicz and Menger properties of filters considered topologically as subspaces of with the Cantor set topology.
Let () be the -ring of all (bounded) real-measurable functions on a -measurable space , let be the family of all such that is compact, and let be all that is compact for any . We introduce realcompact subrings of , we show that is a realcompact subring of , and also is a realcompact if and only if is a compact measurable space. For every nonzero real Riesz map , we prove that there is an element such that for every if is a compact measurable space. We confirm...