36th Summer Topology Conference

July 18-22, 2022

University of Vienna, Department of Mathematics
Oskar-Morgenstern-Platz 1, 1090 Vienna, AUSTRIA

"On strictly point $\mathcal{T}$-asymmetric continua"

Macias, Sergio

A continuum is a compact, connected, metric space. Given a continuum $X$, we define Professor Jones' set function $\mathcal{T}$ as follows \begin{multline*} \mathcal{T}(A)=X\setminus\{x\in X\ |\ \hbox{ there exists a subcontinuum } W\ \hbox{of}\ X\ \hbox{such that}\ \hbox{ $x\in Int(W)\subset W\subset$ $X\setminus A$}\}. \end{multline*} A continuum $X$ is strictly point $\mathcal{T}$-asymmetric provided that for each pair of distinct points $p$ and $q$ of $X$ with $p\in\mathcal{T}(\{q\})$, we have that $q\in X\setminus\mathcal{T}(\{p\})$. We characterize the class of continua which are strictly point $\mathcal{T}$-asymmetric and consider, the particular case, of the class of dendroids (A dendroid is an arcwise connected continuum for which the intersection of two of its subcontinua is connected).

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