Timeline for A space with countable tightness which is not a Fréchet space?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 10, 2013 at 16:14 | vote | accept | Vahideh Bagheri | ||
| Sep 6, 2013 at 15:37 | comment | added | Ramiro de la Vega | @VahidehBagheri: If $x$ is a weak $P$-point then $x$ is not in the closure of any countable $A \subseteq X \setminus \lbrace x \rbrace$ and therefore (using countable tightness) it is not in the closure of $X \setminus \lbrace x \rbrace$; that is, $x$ is isolated. The other implications: Isolated $\Rightarrow$ $P$-point $\Rightarrow$ weak $P$-point are obviously true in any space (never mind the tightness). | |
| Sep 6, 2013 at 15:04 | comment | added | Vahideh Bagheri | [quote]First note that in a space with countable tightness: $P$-point $\Leftrightarrow$ weak $P$-point $\Leftrightarrow$ Isolated point.[\quote] Dear Ramiro de la Vega, I don't find above proposition in literatures. please refer me to that refrense. | |
| Sep 2, 2013 at 8:07 | comment | added | Vahideh Bagheri | Thank u dear. This example was that I wish. Do you know QP-spaces? (spaces X that C(X) has no prime z-ideal except primes and maximals.) This space is a poinwise QP-space. | |
| Aug 22, 2013 at 16:02 | history | answered | Ramiro de la Vega | CC BY-SA 3.0 |