Inverse limits of set-valued functions

The aim of this paper is to understand the classical concept of inverse limit and its generalization in the form of inverse limit of polynomial functions. The concept of inverse limits appeared in the 1920s. It is an elegant theoretical tool for constructing mathematical objects with unusual properties. The inverse limit of simple objects can be disproportionately more complicated. In 2004, a generalization of inverse limits was first used for polynomial mappings, which is the main subject of this paper. The latter will contain an understandable interpretation of inverse limits and proofs of the most important theorems. The usefulness of the notion will be illustrated with examples.

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• INGRAM, W. T. a MAHAVIER, William S. Inverse Limits: from continua to chaos. [1st ed.]. Developments in Mathematics. London: Springer, 2012. ISBN 978-1-4614-1796-5.