Inverse Limits with Smith Functions
Keywords:
connectedness, continuum theory, indecomposability, indecomposable continua, inverse limits with set-valued functions, Smith functionsAbstract
We call an upper semi-continuous function $f:[0,1] \rightarrow 2^{[0,1]}$ a Smith function if $f$ is surjective, the graph of $f$ is connected, and the graph of $f$ is the union of finitely many vertical and horizontal line segments. We introduced the definition of a Smith function (named in honor of Michel Smith) at the 2021 Spring Topology and Dynamical Systems Conference. In this paper, we present various theorems about inverse limits whose bonding functions are Smith functions. We focus on the connectedness and indecomposability of such inverse limits, but some other topics are discussed as well. Numerous examples and open problems are also provided.
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