Talk:Equivalence of Definitions of Compact Topological Subspace

I still have a problem with this.

From the definition, $T_A$ is compact iff all open covers $\mathcal C \subseteq T_A$ have a finite subcover for $T_A$. That is, $T_A$ being defined as compact in itself.

Then we have that $T_A$ is compact in iff all open covers $\mathcal C \subseteq T$ have a finite subcover.

But the latter is not specified anywhere in the definition of subspace and therefore confuses the reader because he's going to be looking everywhere for that definition.

I understand that because it's an iff that both sides of the iff can be used as a definition, but the RHS of the iff is currently not so used.

Would this be clearer if (a) we included this "equivalent definition" on the Compact Subspace page, (b) linked to that page from here (we're currently linking to the "Compace Space" page) and (c) expressed this condition in symbols as well as words? --prime mover (talk) 09:07, 24 November 2012 (UTC)

I'd say (a) is very important (I always use the latter definition), (b) should be done, and I'm not sure if (c) will bring clarification; the reader unfamiliar with the symbology and terminology will likely consult the "cover/open cover" page, and no problem occurs. --Lord_Farin (talk) 09:20, 24 November 2012 (UTC)

How does that work, then? (From a structural point of view, I mean - the proof itself is lacklustre.) --prime mover (talk) 21:57, 27 November 2012 (UTC)

I consider it accurately dealt with in the current set-up, as you adhered to both (a) and (b). Or did you mean something else? --Lord_Farin (talk) 22:51, 27 November 2012 (UTC)

no, that's what I meant --prime mover (talk) 22:59, 27 November 2012 (UTC)