Timeline for Product of posets with Hausdorff interval topology
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 22, 2017 at 12:44 | vote | accept | Dominic van der Zypen | ||
| Nov 22, 2017 at 12:44 | comment | added | Dominic van der Zypen | That's right, thanks for the picture! | |
| Nov 22, 2017 at 12:43 | comment | added | Todd Trimble | My linked answer says that subbasis elements like $\pi^{-1}(U)$ are not open in the interval topology, because $\pi_1^{-1}(U)$ is too small to contain any union of a northwest quadrant and a southeast quadrant (and any basic in the interval topology contains such a union). In brief, your displayed formula for $U$ is incorrect. Try drawing a picture of a $P \setminus (\uparrow (x, y))$, which looks like a complement of a northeast quadrant (i.e., looks like a "thick L-shape"), and you should see this easily. | |
| Nov 22, 2017 at 12:29 | comment | added | Dominic van der Zypen | But why is every subbasic set of the product topology $\tau_p$ open in the interval topology (see my (non-)answer, starting from "Conversely") | |
| Nov 22, 2017 at 11:03 | history | answered | Todd Trimble | CC BY-SA 3.0 |