7 papers
Gears and pulleys in non-Euclidean space forms
Heleno S. Cunha, Lucas H. R. de Souza, Sergio A. P. Prado
In this article we study, in their non-Euclidean versions, two important mechanical systems that are very common in numerous devices. More precisely, we study the laws governing th…
Spaces where all bijections are morphisms
Lucas H. R. de Souza
Here we classify all topological spaces where all bijections to itself are homeomorphisms. As a consequence, we also classify all topological spaces where all maps to itself are co…
Constructing Bowditch boundaries of some relatively hyperbolic groups that are homeomorphic to the -dimensional Sierpiński carpet
Lucas H. R. de Souza
In this paper we prove that if some relatively hyperbolic groups have Bowditch boundary homeomorphic to the -sphere, then they are also relatively hyperbolic with respect to ano…
Some properties that are preserved by transferring boundary functors
Lucas H. R. de Souza
If a Hausdorff locally compact paracompact space has a coarse structure, then there is a family of well behaved compactifications associated to it. If there are two of these spaces…
Characterization of the -dimensional Sierpiński carpet as an inverse limit of closed balls
Lucas H. R. de Souza
In this paper we generalize, for any dimension, a theorem of Tshishiku and Walsh that characterizes the Sierpiński carpet as a limit set of maps from the disc to the sphere.
Equivariant blowups of bounded parabolic points
Lucas H. R. de Souza
Let be a group acting by homeomorphisms on a Hausdorff compact space . We constructed a new space that blows up equivariantly the bounded parabolic points of . This m…