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| 22 May 2024 |
 gm_z | it's kind of strange that colimits of compact spaces isn't necessarily compact, but colimits of compactly generated spaces is compactly generated | 15:05:24 |
| gm_z | does anyone have any intuition for this | 15:05:30 |
| 23 May 2024 |
| cas [they/them] | In reply to @gm_z:matrix.org
it's kind of strange that colimits of compact spaces isn't necessarily compact, but colimits of compactly generated spaces is compactly generated Isn't the topology of a compactly generated space defined by a family of maps into it? | 17:34:28 |
| cas [they/them] | Taking colimits should preserve this according to my intuition | 17:35:30 |
 somenick | hello. i'm stalled with notation learning algebraic topology. Would anybody know, what i_x0 and i_x1 can mean here? | 17:47:28 |
| somenick | 
Download 1713366580053.jpg | 17:48:14 |
| gm_z | In reply to @quantum:envs.net
Isn't the topology of a compactly generated space defined by a family of maps into it? hm which family of maps? | 18:21:19 |
| gm_z | In reply to @somenick:matrix.org
hello. i'm stalled with notation learning algebraic topology. Would anybody know, what i_x0 and i_x1 can mean here? i_{x_0} \colon I \to X is the constant map t \mapsto x_0, likewise for i_{x_1} | 18:22:05 |
| cas [they/them] | In reply to @gm_z:matrix.org
hm which family of maps? All functions K -> X where K is compact | 18:24:24 |
| cas [they/them] | Iirc the definition of a compactly generated space is one where the topology on that space is the final topology for some given set of functions K -> X | 18:25:59 |
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