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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$\kappa$-topologies for right topological semigroups
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by John Baker, Neil Hindman and John Pym PDF
Proc. Amer. Math. Soc. 115 (1992), 251-256 Request permission

Abstract:

Given a cardinal $\kappa$ and a right topological semigroup $S$ with topology $\tau$, we consider the new topology obtained by declaring any intersection of at most $\kappa$ members of $\tau$ to be open. Under appropriate hypotheses, we show that this process turns $S$ into a topological semigroup. We also show that under these hypotheses the points of any subsemigroup $T$ with card $T \leq \kappa$ can be replaced by (new) open sets that algebraically behave like $T$. Examples are given to demonstrate the nontriviality of these results.
References
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 115 (1992), 251-256
  • MSC: Primary 22A15
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1093590-5
  • MathSciNet review: 1093590