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> Let A be a subset of a topological space $X$, and let $O$ be a collection of subsets of $X$.  
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>  (i) The collection $O$ is said to cover $A$ or to be a cover of $A$ if $A$ is contained in the union of the sets in $O$.  
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>  (ii) If $O$ covers $A$, and each set in $O$ is open, then we call $O$an open cover of $A$.  
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>  (iii) If $O$ covers $A$, and $O'$ is a subcollection of $O$ that also covers A, then $O'$ is called a subcover of $O$.(Topology: Pure and Applied, Adams 206)
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In the example/question I am asking, the topological is being generated by $B=\{(–a,a)\ s.t.\ a \in \mathbb{R}\}$. Thus, $(-1,1)$ would have a finite subcover as would a closed interval, say $[-3,3]$.

But what about a half open interval like $(1,4]$ or $[–3,1)$? Would they be compact and have a finite subcover?