arXiv subjects

Bryant Rosado Silva

Publications and source records attributed to Bryant Rosado Silva.

2 recordsLinked to original sources

arXiv2025

Generically hereditarily equivalent continua and topological characterization of generic maximal chains of generalized Ważewski dendrites

The notion of hereditarily equivalent continua is classical in continuum theory with only two known nondegenerate examples (arc, and pseudoarc). In this paper we introduce generically hereditarily equivalent continua, i.e. continua which are homeomorphic to comeager many subcontinua. We investigate this notion in the realm of Peano continua and we prove that all the generalized Ważewski dendrites are such. Consequently, we study maximal chains consisting of subcontinua of generalized Ważewski dendrites and we prove that there is always a generic orbit under the homeomorphism group action. As a part of the proof we provide a topological characterization of the generic maximal chain.

math.GN↗

arXiv2022

Path-Connectedness of the Hyperspace of Compact Subsets of $\mathbb{R}^n$

When one considers the collection $\mathcal{H}(\mathbb{R}^n)$ of all compact subsets of $\mathbb{R}^n$ and equip it with a topology, many questions can be asked about the topological space one ends up with. This is an example of a hyperspace, a mathematical object which has been studied in a more abstract setting since the beginning of the 20th century. Here we give an elementary proof of the path-connectedness of $\mathcal{H}(\mathbb{R}^n)$, with the topology induced by the Hausdoff metric, by exploring the vector structure of $\mathbb{R}^n$ and using only basic ideas of topology of metric spaces that undergraduate students with just a basic knowledge of these concepts will be able to understand.

math.GN↗