Talk:Compactly generated space

mixed up concepts

I think that Hausdorff compactly generated spaces and compactly generated spaces are mixed in the entry. For example, by definition every compactly generated space is T1 (the points are closed), and there are non T1 spaces verifying the first axiom of countability, so it is not true that every space verifying the first axiom of countability is compactly generated. Espigaymostaza (talk) 16:13, 10 March 2009 (UTC)

Hausdorff-compactly generated

@Kaba3: I can't seem to find any reference in the literature for the terminology "Hausdorff-compactly generated" that you introduced in the article. I understand the need to distinguish between different concepts, but is that a term that you just made up for the article?

Also, do you have any source using that concept (even if not by name)? As you know, there are many variants of the notion of compactly generated or k-space around. They are defined as final topology with respect to either the inclusions from a bunch of subspaces, or with respect to all continuous maps from any spaces with certain properties. When the Hausdorff property is thrown into the mix, one usually considers the family of all continuous maps from compact Hausdorff spaces, not the family of the inclusions of all compact Hausdorff subspaces. I think the two notions are different. PatrickR2 (talk) 19:35, 23 February 2023 (UTC)

P-generated, where P is a set of subsets, means having the P-determined / P-coherent / P-generated topology as described in Coherent topology. Compactly generated means P-determined topology with P = compact subsets. Hausdorff-compactly generated means P-determined topology with P = compact and Hausdorff subsets. So I just substituted P there. If you think something is confusing or can be said better go ahead and make it better :) Kaba3 (talk) 18:06, 26 February 2023 (UTC)

Thanks for the explanation. I understand perfectly what you did, but Wikipedia is supposed to reflect commonly held knowledge and this new terminology may be construed as WP:OR, which unfortunately is not acceptable here. See also the discussion in https://math.stackexchange.com/questions/4646084/unraveling-the-various-definitions-of-k-space-or-compactly-generated-space. As currently presented, I think the article gives undue emphasis to your notion of "Hausdorff-CG" and completely ignores the more important cases of final topologies with respect to continuous maps from arbitrary topological spaces satisfying some property. At some point, I would like to expand and reorganize the article to add this information, as well as deemphasize the "Hausdorff-CG" notion. Please let me know if you have any objection.

Also FYI, as you can see in some of the edits I have made recently, there were some incorrect statements regarding your notion. It was not correct to add "(Hausdorff)" everywhere and expect that things valid without "(Hausdorff)" would remain so. PatrickR2 (talk) 19:58, 26 February 2023 (UTC)

@Kaba3: As we discussed, I have rewritten the lead and the Definitions section to better reflect the range of definitions that occur in the literature and to deemphasize the notion of "Hausdorff-CG" (Def 3), which is the least useful of the three defs. After you get the chance to read it, please let me know what you think.

I have not touched the other sections, but what remains to be done is to double check and justify with references each of the assertions in the Examples and Properties sections, as well as expand them to cover the three definitions if possible. I'll get to it at some point, or you could maybe help out on this if you have the time? Not exactly sure at the moment what the best presentation would be. We don't want to use a generic name like just "compactly generated", which is ambiguous. And we don't really want to repeat everywhere some long-winded phrases like "compactly generated by maps from compact Hausdorff spaces", etc. to distinguish the cases. And also "Hausdorff-compactly generated" is not really appropriate as it is WP:OR, but mostly it's too easy to confuse with spaces that are "Hausdorff compactly generated" (without the hyphen). One idea would be to have a table of local abbreviations "CG-1" = "coherent with compact subspaces", "CG-2" = etc at the top of the Examples section and same at the top of Properties, and then use that in these sections. Not sure. Maybe you have a better idea? Regards. PatrickR2 (talk) 04:29, 4 March 2023 (UTC)

@Kaba3: Hi. Did you have any comments on the above? PatrickR2 (talk) 16:42, 11 March 2023 (UTC)

@PatrickR2 Hey! I don't know what to do, but I agree that the different variations would be good to separate. I also agree that long names are difficult to use, so your abbreviation idea sounds good. Feel free to modify my modifications, I'm mostly busy with other stuff right now. Kaba3 (talk) 18:27, 20 March 2023 (UTC)

I had time to read more detailedly. I like your changes. I think the page is on its way to a clearer one. Kaba3 (talk) 18:36, 20 March 2023 (UTC)

Thanks for checking it. I'll modify more things when I can find some time. Some of the existing items in the Examples and Properties sections may need to be corrected or expanded. And at least find relevant literature references for each fact/example. Thanks again. PatrickR2 (talk) 23:18, 20 March 2023 (UTC)

I had email-notifications for mentions disabled for some reason; now enabled. Kaba3 (talk) 19:07, 20 March 2023 (UTC)

@Kaba3: Hi. I finally reorganized the Examples and Properties sections. Would appreciate if you could take a look at your convenience. Thank you. PatrickR2 (talk) 04:39, 3 June 2023 (UTC)

Unfortunately someone has somewhat "vandalized" the contribution by removing all math stackexchange references. I'll bring this up for projectwide discussion. See User talk:PatrickR2#Compactly generated space. PatrickR2 (talk) 19:21, 3 June 2023 (UTC)

Please read WP:NOTVANDALISM, such accusation are not appropriate. If you have an issue raise it at WP:RSN as I previously stated. -- LCU ActivelyDisinterested ∆transmissions∆ °co-ords° 22:15, 3 June 2023 (UTC)

Please don't worry too much. That why I put "vandalized" in parentheses and qualified it with the word "somewhat. Apologies for the strong words. PatrickR2 (talk) 23:41, 3 June 2023 (UTC)

Different institutions have different cultural and social norms, I would suggest not using "vandalised" in any sense until you understand how it's used on Wikipedia. -- LCU ActivelyDisinterested ∆transmissions∆ °co-ords° 08:47, 4 June 2023 (UTC)

@PatrickR2 Hi. I think this page has improved substantially. I like how it explicitly untangles all the variations. Thanks for your efforts! Kaba3 (talk) 22:02, 3 June 2023 (UTC)

Thanks a lot. Based on the rest of the article, can you take a look at the section "k-ification" at the end and rework it as necessary? In particular the paragraph starting with The above discussion applies .... I am not sure how it fits with CG-1,2,3, and what is even correct or incorrect here. (and also due to "Hausdorff-compactly generated" meaning CG-3, but is this really what you meant?) It's very unclear to me. Do you have any sources for this? If not, maybe the whole paragraph should be scrapped and we should focus on adding facts and references for what is known from reputable sources. PatrickR2 (talk) 22:48, 6 June 2023 (UTC)

@Kaba3 Hi. Pinging you if you have not seen the above. PatrickR2 (talk) 02:30, 29 June 2023 (UTC)

k-ification section cleanup

In the k-ification section, the paragraph about "Hausdorff-compactly generated" is completely unsourced, and as discussed already with editor @Kaba3: above, it does not make much sense mathematically. Unless someone has a convincing argument against this, I plan to remove it in the near future. Suitable information could be added in the future if someone takes the time to investigate what makes sense in this context and provides reliable sources for it. PatrickR2 (talk) 06:20, 4 September 2023 (UTC)

This has been cleaned up for now. PatrickR2 (talk) 04:47, 7 September 2023 (UTC)