Surjectivity for distal continuous functions on a compact metric space

Question

Where can I find a proof that a distal continuous function of a compact metric space is surjective?

PS: The person asking the question Is there an elementary proof that distal maps are invertible? says he knows two proofs that use the enveloping semigroup, and the Stone-Čech compactification. I am interested in the references where I can find those proofs

Does this answer your question? https://mathoverflow.net/questions/393648/is-there-an-elementary-proof-that-distal-maps-are-invertible — Joseph Van Name, May 15 '22 at 18:47
The person asking the question says he knows two proofs that use the enveloping semigroup, and the Stone-Čech compactification. I am interested in the references where I can find those proofs. — J.C., May 15 '22 at 19:05

score 1 · Answer 1 · answered May 18 '22 at 13:39

1

OP here! The Stone Cech proof can be found on page 33 of Bergelson’s survey on Ergodic Ramsey theory.

The enveloping semigroup proof can be found on page 60 of Brown’s book Topological Dynamics and Ergodic Theory.

answered May 18 '22 at 13:39

Nate River

4,832

Thank you, indeed i found the proofs in those references, furthermore, in the Bergelson’s survey the author refers to the article "Ebrahim Salehi and David B. Ellis. Problems and Solutions: Solutions: Revivals: 6612. Amer. Math. Monthly". Where we can found the enveloping semigroup proof . – J.C. May 25 '22 at 23:14

Surjectivity for distal continuous functions on a compact metric space

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