$\kappa$-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
- J. W. Baker and P. Milnes, The ideal structure of the Stone-Čech compactification of a group, Math. Proc. Cambridge Philos. Soc. 82 (1977), no. 3, 401–409. MR 460516, DOI 10.1017/S0305004100054062
- John F. Berglund, Hugo D. Junghenn, and Paul Milnes, Analysis on semigroups, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, Inc., New York, 1989. Function spaces, compactifications, representations; A Wiley-Interscience Publication. MR 999922
- W. W. Comfort and S. Negrepontis, The theory of ultrafilters, Die Grundlehren der mathematischen Wissenschaften, Band 211, Springer-Verlag, New York-Heidelberg, 1974. MR 0396267, DOI 10.1007/978-3-642-65780-1
- Eric K. van Douwen, The Čech-Stone compactification of a discrete groupoid, Topology Appl. 39 (1991), no. 1, 43–60. MR 1103990, DOI 10.1016/0166-8641(91)90074-V
- Neil Hindman, The ideal structure of the space of $\kappa$-uniform ultrafilters on a discrete semigroup, Rocky Mountain J. Math. 16 (1986), no. 4, 685–701. MR 871030, DOI 10.1216/RMJ-1986-16-4-685 —, Ultrafilters and Ramsey theory—an update, Set Theory and its Applications, (V. Steprans and S. Watson, eds.) Lecture Notes in Math., vol 1401, Springer-Verlag, New York, 1989, pp. 97-118. —, The semigroups $\beta \mathbb {N}$ and its applications to number theory, The Analytical and Topological Theory of Semigroups, (K. H. Hofmann et al, eds.), de Gruyter, Berlin, 1990, pp. 347-360.
- John Pym, Footnote to a paper of J. W. Baker and P. Milnes: “The ideal structure of the Stone-Čech compactification of a group” (Math. Proc. Cambridge Philos. Soc. 82 (1977), no. 3, 401–409), Math. Proc. Cambridge Philos. Soc. 85 (1979), no. 2, 315. MR 516090, DOI 10.1017/S0305004100055729
- Russell C. Walker, The Stone-ÄŚech compactification, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 83, Springer-Verlag, New York-Berlin, 1974. MR 0380698, DOI 10.1007/978-3-642-61935-9
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