Abstract Almost s s -mappings and almost compact mappings have been introduced studied. In this article, we continue to research some questions related the -images (resp., images) of metric spaces. The following results are obtained. (1) A space X X is a quotient image if only sequential having c</m:...

We investigate two properties and their connection to the property of pseudoradiality in the context of compact spaces. The first is the WAP property introduced by P. Simon and the second is the א0-pseudoradial property introduced by B. Šapirovskii. We show that ♦ implies there is a compact space which is pseudoradial but not WAP. We show that there is a model in which CH fails and in which all...

We show that, under certain natural assumptions, large random plane bipartite maps with a boundary converge after rescaling to a one-parameter family (BDL, 0 < L < ∞) of random metric spaces homeomorphic to the closed unit disk of R2, the space BDL being called the Brownian disk of perimeter L and unit area. These results can be seen as an extension of the convergence of uniform plane quadrangu...

This paper deals with questions of how many compact subsets of certain kinds it takes to cover the space ω of irrationals, or certain of its subspaces. In particular, given f ∈ (ω\{0}), we consider compact sets of the form Q i∈ω Bi, where |Bi| = f(i) for all, or for infinitely many, i. We also consider “n-splitting” compact sets, i.e., compact sets K such that for any f ∈ K and i ∈ ω, |{g(i) : ...