36th Summer Topology Conference

July 18-22, 2022

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

"Rigid continua and their inverse limits"

Kac, Teja

We give mapping theorems for certain families of rigid continua; i.e., we give a mapping theorem for stars, paths and cycles of Cook continua. We also introduce the degree of rigidity of a continuum, the notion of $\frac{1}{n}$-rigid continua and provide some existence theorems for $\frac{1}{n}$-rigid continua. We also construct a non-trivial infinite family of pairwise non-homeomorphic continua $X$ with the property that for any sequence $(f_n)$ of continuous surjections $f_n:X\rightarrow X$, the inverse limit $\varprojlim\{X,f_n\}_{n=1}^{\infty}$ is homeomorphic to $X$. Explicitly, we show that for each positive integer $n$, every $\frac{1}{n}$-rigid continuum has this property.

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