Title

A Compact Minimal Space Whose Cartesian Square Is Not Minimal

Author(s)

Jan P. Boronski, AGH University of Science and Technology, KrakowFollow
Alex Clark
Piotr Oprocha

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 {hⁿ(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.

Comments

This document is available for download with the permission of the presenting author and the organizers of the conference. Permission documentation is on file.

Technological limitations may prevent some mathematical symbols and functions from displaying correctly in this record’s metadata fields. Please refer to the attached PDF for the correct display.

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