J. M. R. Sanjurjo

Learn More
In this paper we use the Hausdorff metric to prove that two compact metric spaces are homeomorphic if and only if their canonical complements are uniformly homeomorphic. So, we take one of the two steps needed to prove that the difference between the homotopical and topological classifications of compact connected ANRs depends only on the difference between(More)
Suppose φ : M × R −→ M is a continuous flow on a locally compact metrizable space M and K is an (asymptotically stable) attractor. Let D = ∂A(K) be the boundary of the basin of attraction of K. In the present paper it will be shown how the Conley index of D plays an important role in determining the topological nature of D and allows one to obtain(More)
We prove that two countable locally finite-by-abelian groups G,H endowed with proper left-invariant metrics are coarsely equivalent if and only if their asymptotic dimensions coincide and the groups are either both finitely generated or both are infinitely generated. On the other hand, we show that each countable group G that coarsely embeds into a(More)
Let M be a locally compact metric space endowed with a continuous flow φ : M × R → M . Assume that K is a stable attractor for φ and P ⊆ A(K) is a compact positively invariant neighbourhood of K contained in its basin of attraction. Then it is known that the inclusion K ↪→ P is a shape equivalence and the question we address here is whether there exists(More)
We study dynamical and topological properties of the singularities of continuations of attractors of flows on manifolds. Despite the fact that these singularities are not isolated invariant sets, they share many of the properties of attractors; in particular, they have finitely generated Čech homology and cohomology, and they have the Čech homotopy type of(More)
  • 1