Summer Conference on Topology and Its Applications

Document Type

Plenary Lecture

Publication Date


Publication Source

32nd Summer Conference on Topology and Its Applications


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.


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