Weakly α-favourable measure spaces

F U N D a M E N T a Mathematicae 165 (2000) Weakly Α-favourable Measure Spaces

I discuss the properties of α-favourable and weakly α-favourable measure spaces, with remarks on their relations with other classes.

Embedding measure spaces

‎For a given measure space $(X,{mathscr B},mu)$ we construct all measure spaces $(Y,{mathscr C},lambda)$ in which $(X,{mathscr B},mu)$ is embeddable‎. ‎The construction is modeled on the ultrafilter construction of the Stone--v{C}ech compactification of a completely regular topological space‎. ‎Under certain conditions the construction simplifies‎. ‎Examples are given when this simplification o...

ε-weakly Chebyshev subspaces and quotient spaces

Weakly Continuously Urysohn Spaces

We study weakly continuously Urysohn spaces, which were introduced in [Z]. We show that every weakly continuously Urysohn w∆-space has a base of countable order, that separable weakly continuously Urysohn spaces are submetrizable, hence continuously Urysohn, that monontonically normal weakly continuously Urysohn spaces are hereditarily paracompact, and that no linear extension of any uncountabl...

On weakly bisequential spaces

Weakly bisequential spaces were introduced by A.V. Arhangel’skii [1], in this paper. We discuss the relations between weakly bisequential spaces and metric spaces, countably bisequential spaces, Fréchet-Urysohn spaces.