Talk:Closed Subspace of Compact Space is Compact

This might be more of a language question than anything else, but isn't any subspace closed (and open) as a space itself? Shouldn't we say something like "a subspace that, when seen as a subset of the larger space, is closed"? When we say "(adjective) subspace", I always think that the adjective refers to the subspace as a space in its own right, and in this case, any subspace of any space would be closed (and open) subspace, by the definition of topology. Otherwise it seems the meaning changes based on the presence of the prefix "sub-", in which case the meaning of the adjective isn't self-contained within the syntagm, but rather dependent on the ambient space. --plammens (talk) 10:45, 25 September 2021 (UTC)

I have expanded upon the exposition, and clarified the presentation. Thank you for your attention to detail. --prime mover (talk) 11:05, 25 September 2021 (UTC)