Topological order complexes and resolutions of discriminant sets.
Let be the space of all lower semi-continuous extended real-valued functions on a Hausdorff space , where, by identifying each with the epi-graph , is regarded the subspace of the space of all closed sets in with the Fell topology. Let We show that is homeomorphic to the Hilbert cube if and only if is second countable, locally compact and infinite. In this case, it is proved that is homeomorphic to (resp. ) if is compact (resp. is non-compact), where is the cone over...
We study and classify topologically invariant σ-ideals with an analytic base on Euclidean spaces, and evaluate the cardinal characteristics of such ideals.
The focus of this paper are questions related to how various geometric and analytical properties of hyperbolic 3-manifolds determine the commensurability class of such manifolds. The paper is for the large part a survey of recent work.
We introduce two new classes of compacta, called trees of manifolds with boundary and boundary trees of manifolds with boundary. We establish their basic properties.
A proof is given that, with the only exception of (3,2), all toroidal knots in R3 obtained in the standard way by stereographic projection of knots in S3 have tritangent planes.