Timeline for A basic question on Stone-Cech compactification of $\mathbb{Z}$
Current License: CC BY-SA 3.0
10 events
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| Mar 27, 2014 at 13:57 | comment | added | Ben Barber | @Alvin, could you add some details as an answer for people who come across this in future? | |
| Sep 29, 2012 at 5:25 | comment | added | Yemon Choi | In response to Simon Henry: well, Safoura and I belong to the tradition that immediately shout "Arens products on the second dual of the group algebra". ;) | |
| Sep 29, 2012 at 5:24 | comment | added | Yemon Choi | I have to disagree with jbc. The perspective "let's only look at compactifications which are groups" would ignore a whole bunch of interesting and actively studied semigroup compactifications (WAP and LUC being the obvious ones). | |
| Sep 25, 2012 at 13:13 | comment | added | Andreas Blass | I agree with Justin's suggestion to see the book of Hindman and Strauss, "Algebra in the Stone-Cech Compactification". I suspect the answer to your question isn't known, but if it is (or, rather, if it was a few years ago) then this book would very probably contain it. | |
| Sep 25, 2012 at 11:55 | comment | added | Justin Moore | There is a standard definition. A set X is in U+V iff {i in Z : {j in Z : i+j in X} in V} in U. See Hindman and Strauss's book or either of the following books by Todorcevic: "Topics in Topology", "introduction to Ramsey Spaces." | |
| Sep 25, 2012 at 8:35 | comment | added | jbc | If you are interested in algebraic structures on the compactification of a topological group (here the whole numbers as a discrete group) then I would suggest that perhaps you should look at the Bohr rather than the Stone-Cech compactification | |
| Sep 25, 2012 at 7:33 | comment | added | Simon Henry | That might be a silly question but : what is the semi group structure on $\beta \mathbb{Z}$ ? as far as i know cartesian product of ultrafilter are no longer ultrafilter, so the sum of two ultrafilter has no reason to be an ultrafilter in general ? | |
| Sep 25, 2012 at 2:42 | history | edited | Alvin | CC BY-SA 3.0 |
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| Sep 24, 2012 at 21:14 | history | edited | Alvin | CC BY-SA 3.0 |
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| Sep 24, 2012 at 19:22 | history | asked | Alvin | CC BY-SA 3.0 |