**"Rigid continua and their inverse limits"**
#### Kac, TejaWe 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. |