Non-archimedean topological monoids

M. Megrelishvili, M. Shlossberg

Research output: Contribution to journalArticlepeer-review

Abstract

We say that a topological monoid S is left non-archimedean (in short: l-NA) if the left action of S on itself admits a proper S-compactification ν:S↪Y such that Y is a Stone space. This provides a natural generalization of the well known concept of NA topological groups. The Stone and Pontryagin dualities play a major role in achieving useful characterizations of NA monoids. We show that many naturally defined topological monoids are NA and present universal NA monoids. Among others, we prove that the Polish monoid C(2ω,2ω) is a universal separable metrizable l-NA monoid and the Polish monoid NN is universal for separable metrizable r-NA monoids.

Original languageEnglish
Pages (from-to)597-625
Number of pages29
JournalSemigroup Forum
Volume109
Issue number3
DOIs
StatePublished - Dec 2024

Keywords

  • Compactifiable monoid
  • Equivariant compactification
  • Non-archimedean monoid
  • Pontryagin duality
  • Stone duality

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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