Timeline for Category of topological spaces with open or closed maps
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Dec 5 at 14:47 | history | edited | LSpice | CC BY-SA 4.0 |
Proofreading, while this is on the front page (sadly, rotted link wasn't Wayback'd)
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| Dec 5 at 4:52 | comment | added | Martin Sleziak | The link to christianmarks.wordpress.com/category/bagatelle now seems to be dead - and I did not find anything useful in the Wayback Machine, either. | |
| Sep 8 at 23:55 | answer | added | James E Hanson | timeline score: 8 | |
| Jan 8, 2013 at 20:07 | history | edited | Adam Epstein | CC BY-SA 3.0 |
Elaboration concerning products in the category with open maps.; added 1 characters in body; added 1 characters in body
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| Jan 3, 2013 at 21:13 | comment | added | Todd Trimble | If you're asking why doesn't the usual cartesian product with the usual projections give you cartesian products with respect to open maps, consider this example. Open maps $Z \to X \times X$ ought then to be in natural bijection with pairs of open maps $f: Z \to X$, $g: Z \to X$ given by composing with projections. In particular, there ought to be an open map $X \to X \times X$ corresponding to the pair $f = 1_X$, $g = 1_X$; set−theoretically this would be the diagonal map. But the diagonal isn′t open unless X$ is discrete. So the projections, while open, don't realize the universal property. | |
| Jan 3, 2013 at 20:16 | history | edited | Adam Epstein | CC BY-SA 3.0 |
Query regarding products
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| Jan 3, 2013 at 20:10 | comment | added | Adam Epstein | I'm probably missing something obvious, but why don't products typically exist in the category with open maps? The projections from the usual product (in the category with continuous maps) are open, yielding a canonical open map from the usual product to the putative unusual product. After this I am stuck. | |
| Jan 1, 2013 at 18:26 | answer | added | Todd Trimble | timeline score: 12 | |
| Dec 26, 2012 at 20:36 | comment | added | Adam Epstein | Regarding the category whose morphisms are open maps, there are a few remarks here: christianmarks.wordpress.com/category/bagatelle For example, it is asserted that all coproducts exist, that not all products exist, and that "something analogous to powers of a single space" exists. | |
| Dec 25, 2012 at 17:43 | answer | added | David Carchedi | timeline score: 6 | |
| Dec 25, 2012 at 11:35 | comment | added | Pietro Majer | I think he means what he wrote, namely, to what extent these three categories differ, taking into account that they have the same objects ands the same isomorphisms. | |
| Dec 25, 2012 at 0:17 | comment | added | Zhen Lin | The isomorphisms in the category of topological spaces and continuous maps are precisely the homeomorphisms. Did you mean to say "bijection" instead of "isomorphism"? | |
| Dec 25, 2012 at 0:01 | history | asked | Adam Epstein | CC BY-SA 3.0 |