arXiv subjects

Mauricio Chacón-Tirado

Publications and source records attributed to Mauricio Chacón-Tirado.

2 recordsLinked to original sources

arXiv2024

Connectivity degrees of complements of closed sets in continua

In the literature, various types of points and meager sets whose complements are connected have been studied, such as colocally connected points, non-weak cut points/sets, non-block points/sets, shore points/sets, etc. We extend that study, in the following way: considering a continuum $X$ and a natural number $n$, we investigate sets $A \in 2^X$ meeting the criterion that $X - A$ has at most $n$ components, and we introduce degrees of connectivity of the complement of $A$. When $n=1$ and $A$ is meager or singleton, these new definitions are equivalent to the known definitions of non-cut points/sets.

math.GN↗

arXiv2022

A property equivalent to being semi-Kelley

We present a property equivalent to the property of being semi-Kelley. Using this equivalence we prove that being semi-Kelley is a hereditary property for atriodic continua. We prove that semi-Kelley remainders are atriodic, moreover, we prove that semi-Kelley continua are semi-Kelley remainders for chainable continua, circularly chainable continua, and arc continua, and we give an example of an atriodic Kelley continuum which is a semi-Kelley remainder and not a Kelley remainder. We also prove that hereditarily semi-Kelley dendroids are smooth.

math.GN↗