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Proceedings of the American Mathematical Society

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

 

 

$ \kappa$-topologies for right topological semigroups


Authors: John Baker, Neil Hindman and John Pym
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1093590-5
Article copyright: © Copyright 1992 American Mathematical Society