# Definition talk:Compact Space/Topology/Subspace/Definition 2

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Sutherland, edition 2 defines this as a "compact subset", and using open sets of X, not H. Edition 1 also uses open sets of X, and, strictly speaking, defines it for a subset while saying that he defines it for a subspace. But at this point in the book, Sutherland does not distinguish anymore between subsets and subspaces, so it must not be taken literally. --barto (talk) 10:36, 10 September 2017 (EDT)

- The 1975 edition says:
*With the above notation, $T$ is*compact*if given any cover $\mathcal U$ of $T$ by sets open in $S$, there is a finite subcover of $\mathcal U$ for $T$.*

- $T$ has been defined as:
*a subspace of another topological space $S$.*

- This all matches our current definition. A subspace may be compact, a subset can only be compact if it has a topology imposed upon it, at which point it becomes a subspace. --prime mover (talk) 11:47, 10 September 2017 (EDT)

- I used to be really fit and strong, and I used to be able to tear telephone directories in half. Now I discover I can't even tear a copy of Sutherland in half. --prime mover (talk) 18:05, 10 September 2017 (EDT)