Category talk:Compact Spaces

Why is this a subcategory of Category:Metric Spaces? --abcxyz (talk) 17:11, 11 November 2012 (UTC)

Why should it not be? --prime mover (talk) 19:12, 11 November 2012 (UTC)

Maybe I haven't looked carefully enough, but I thought that a subcategory should be a special case of a category (otherwise why is it called a subcategory?). Not the case? --abcxyz (talk) 19:18, 11 November 2012 (UTC)

There can be compact metric spaces can there not? --prime mover (talk) 21:36, 11 November 2012 (UTC)

Of course, but I meant that $\neg ($compact space $\implies$ metric space$)$. Does that even matter? --abcxyz (talk) 00:03, 12 November 2012 (UTC)

Should it? --prime mover (talk) 06:18, 12 November 2012 (UTC)

Seeing as the category is about compact spaces in the topological sense and not the metric space sense, I'd say it matters. I'd say it should be a subcategory of topology and examples of topologies, but not of metric spaces. --Alec (talk) 21:03, 12 November 2012 (UTC)