Timeline for Maximal ideals and ultrafilters
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 1, 2010 at 17:29 | comment | added | tali | Got it. Thanks again Peter I appreciate it very much. | |
| Aug 1, 2010 at 16:21 | comment | added | Peter Krautzberger | Thinking of $\beta \mathbb{N}$ as the set of all maximal filters, i.e., ultrafilters, on $\mathbb{N}$, the so called Stone topology is generated by basic clopen set of the form $$\bar{A} = \{ F \in \beta \mathbb{N}: \ A \in F \}$$ for every $A\subseteq \mathbb{N}$. | |
| Aug 1, 2010 at 16:17 | comment | added | Peter Krautzberger | Glad I could help. I remember that it confused me when I met filters/ideals for the first time -- to use 'improper' is really improper as Joel David Hamkins pointed out :) | |
| Aug 1, 2010 at 16:17 | comment | added | tali | Thanks a lot Peter! The confusion indeed was caused by the omitting of the word proper in some places. Actually the interest in this terms aroused from trying to understsand the topology on the Stone-Cech compactification \beta(X) of a topological space X. For example, in your example of the space \beta(N), who would be the basic open sets for this topology? | |
| Aug 1, 2010 at 15:49 | history | edited | Peter Krautzberger | CC BY-SA 2.5 |
reaction to Joel's comment
|
| Aug 1, 2010 at 15:36 | comment | added | Peter Krautzberger | Thanks. That is what I meant with 'usually the interest lies' :) But I will try to make this clearer. | |
| Aug 1, 2010 at 15:06 | comment | added | Joel David Hamkins | In many contexts, however, including much of set theory, people use the words filter and ideal to mean what you call proper filter and proper ideal. | |
| Aug 1, 2010 at 14:29 | history | answered | Peter Krautzberger | CC BY-SA 2.5 |