Timeline for A space with independent tightness
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Mar 4, 2022 at 9:11 | comment | added | Santi Spadaro | Tyrone, can you add your comment as an answer? | |
| Feb 25, 2022 at 9:46 | comment | added | Santi Spadaro | Thank you! Actually, the special case you mentioned in your second comment already appears in Gary Gruenhage, "K-spaces and Products of Closed Images of Metric Space", Proceedings of the American Mathematical Society, Vol. 80, n.3 (1980), 478--482. | |
| Feb 23, 2022 at 23:15 | comment | added | Tyrone | In the simplest case $(\bigvee_\omega I)\times\bigvee_{\omega_1}I)$ has countable tightness iff $\mathfrak{b}>\aleph_1$ (here $I=[0,1]$ is the unit interval with wedgepoint $0$). | |
| Feb 23, 2022 at 23:14 | comment | added | Tyrone | Let $X,Y$ be (connected) CW complexes. Then $X\times Y$ is a CW complex iff it is a k-space iff it is sequential iff it has countable tightness (this is due to Tanaka). On the other hand, $X\times Y$ is a CW complex iff one of $X,Y$ has countably many cells and the other has fewer than $\mathfrak{b}$ many cells (this is due to Brooke-Taylor). Here $\mathfrak{b}$ is the bounding number. Thus $\aleph_1\leq\mathfrak{b}\leq2^{\aleph_0}$, and there are models of ZFC in which either or both inequalities are strict, or both are equality. | |
| Feb 23, 2022 at 13:45 | comment | added | Martin Sleziak | I have added (cardinal-characteristics) - usage for topics like this seems to be in accordance with the tag info. I was also considering (independence-results), but since I wasn't sure, I have just mentioned it here in a comment rather than directly editing the tags. | |
| Feb 23, 2022 at 13:44 | history | edited | Martin Sleziak |
added the (cardinal-characteristics) tag - since the question is about tightness; feel free to remove the tag if you don't consider it suitable
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| Feb 23, 2022 at 13:30 | history | edited | Santi Spadaro | CC BY-SA 4.0 |
added 44 characters in body
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| Feb 23, 2022 at 13:15 | history | asked | Santi Spadaro | CC BY-SA 4.0 |