#### Document Type

Plenary Lecture

#### Publication Date

6-2017

#### Publication Source

32nd Summer Conference on Topology and Its Applications

#### Abstract

A compact metric space X is called *minimal* if it admits a minimal homeomorphism; i.e. a homeomorphism h:X→ X such that the forward orbit {h^{n}(x):n=1, 2, ...} is dense in X, for every x ∈ X. In my talk I shall outline a construction of a family of 1-dimensional minimal spaces from "A compact minimal space Y such that its square YxY is not minimal" whose existence answer the following long standing problem in the negative.

**Problem.** Is minimality preserved under Cartesian product in the class of compact spaces?

Note that for the fixed point property this question had been resolved in the negative already 50 years ago by Lopez, and a similar counterexample does not exist for flows, as shown by Dirbák.

#### Copyright

Copyright © 2017, the Authors

#### eCommons Citation

Boronski, Jan P.; Clark, Alex; and Oprocha, Piotr, "A Compact Minimal Space Whose Cartesian Square Is Not Minimal" (2017). *Summer Conference on Topology and Its Applications*. 23.

https://ecommons.udayton.edu/topology_conf/23

## Comments

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