Why do we define compactness via (finite) open covers, why not closed?
121135
Why don't we use closed covers to define compactness of metric space?
55374
Cover of (0,1) with no finite subcover & Open sets of compact function spaces
67279
Is the union of finitely many open sets in an omega-cover contained within some member of the cover?
148187
Question regarding one-point compactification and homeomorphisms
79424
Don't understand proof that interior of a set is open
40682
What's going on with "compact implies sequentially compact"?
29744
Compactness and axiomatisability
106957
Compact sets are closed?
51156
Function is Continuous When Restricted to Closed Sets Which Cover the Space
147331
Compactness and Hausdorffness
127900
Interior of closure of open set in topological space
66334
How is every subset of the set of reals with the finite complement topology compact?
61930
Intersection of Closed and Compact Set is Closed
58948
If $A$ is compact, is then $f(A)$ compact?
94485
Limit point compactness implies compactness.
110957
No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof?
128334
Question regarding open covers in Zariski topology (distinguished opens of affine schemes are quasi-compact)