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Results tagged with topological-semigroups-and-monoids
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Topological semigroups/monoids: topological space endowed with a continuous semigroup/monoid structure, or, equivalently, semigroup/monoid endowed with a compatible topology.
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Why is choice needed in Ellis' Lemma?
Ellis Lemma on idempotent elements asserts that:
Lemma (Ellis). Every compact semigroup has an idempotent.
The proof below is excerpted from Todorcevic's Introduction to Ramsey Spaces, Lemma 2.1.
L …
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