Timeline for Giving $\mathit{Top}(X,Y)$ an appropriate topology
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 1, 2022 at 5:26 | history | edited | David White | CC BY-SA 4.0 |
Fixed badly broken link plus a few typos
|
| Jan 13, 2015 at 9:46 | history | edited | Paul Taylor | CC BY-SA 3.0 |
Added PS about Johnstone and in reply to Tyler Lawson,
|
| Jan 10, 2015 at 19:20 | comment | added | Tyler Lawson | As you haven't really received much response on what our motivations are, let me at least mention that these function spaces and their cartesian-closed properties are absolutely critical to Serre's method for calculating homotopy groups: he uses path spaces to replace a map $X \to Y$ by a nicer map, uses the adjunction to show that this new map is a Serre fibration, and then uses this technique to calculate homotopy groups by "slicing off" one of them at a time (leading to his proofs of finite generation/finiteness). These techniques were so effective that they are now ubiquitous. | |
| Jan 10, 2015 at 14:11 | history | edited | Todd Trimble | CC BY-SA 3.0 |
Corrected a significant typo
|
| Apr 22, 2013 at 19:31 | comment | added | Todd Trimble | Just a little note on local compactness. A lot of texts define this to mean a space such that every point has a compact neighborhood. But this often isn't as "convenient" (to use the word pointedly) as the stronger condition that every point has a basis of compact neighborhoods, which is essentially the interpolation property mentioned above. However, the conditions coincide if the space is assumed to be Hausdorff. | |
| Apr 20, 2013 at 9:38 | vote | accept | Amr | ||
| Apr 20, 2013 at 9:38 | vote | accept | Amr | ||
| Apr 20, 2013 at 9:38 | |||||
| Apr 18, 2013 at 21:12 | history | edited | Paul Taylor | CC BY-SA 3.0 |
more complete story
|
| Apr 17, 2013 at 17:08 | comment | added | johndoe | doesn't Isbell consider the case where I (as in the OP question) might run over the whole category of spaces? In other words, it seems to me that the OP question is a special case of the problem considered in Isbell's survey and might very likely have an affirmative answer. Am I wrong? | |
| Apr 17, 2013 at 14:20 | history | answered | Paul Taylor | CC BY-SA 3.0 |