A bounded coarse structure for families of pseudometrics
We define the bounded coarse structure attached to a family of pseudometrics and give some counterexamples to conjectures that arise naturally.
math.GN↗
arXiv subjects
Jesús P. Moreno-Damas
Publications and source records attributed to Jesús P. Moreno-Damas.
A $C_0$ coarse structure for families of pseudometrics and the Higson-Roe functor
This paper deepens into the relations between coarse spaces and compactifications, by defining a $C_0$ coarse structure attached to a family of pseudometrics. This definition allow us to give a more topological point of view on the relations between coarse structures and compactifications ---like the Higson-Roe compactification, corona and functor and the topological coarse structure attached to a compactification---, define new functors and giving new relations between them, in particular, some equivalences of categories.
math.GN↗
Dugundji's Canonical Covers, asymptotic and covering dimension
Given a nowheredense closed subset $X$ of a metrizable compact space $\tx$, we characterize the dimension of $X$ in terms of the multiplicity of the canonicals covers of the complementary of $X$, specially in some particular cases, like when $\tx$ is the Hilbert cube or the finite dimensional cube and $X$, a Z-set of $\tx$. In this process, we solve some questions in the literature.
math.GN↗