We show that there exists a correspondence between the equivalence classes of coverings of a polyhedron and the equivalence classes of coverings of its poset of simplices. The same is true for a poset and its order complex. ...

Let M be a finite-dimensional manifold and Sigma be a driftless control system on M of full rank. We prove that for a given initial state x epsilon M, the covering space Gamma(Sigma, x) for a monotonic homotopy of trajectories ...

We show that coorbit spaces can be characterized in terms of arbitrary phase-space covers, which are families of phase-space multipliers associated with partitions of unity. This generalizes previously known results for ...

For a topological property P, we say that a space X is star Pif for every open cover Uof the space X there exists Y aS, X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelof spaces establishing, ...