Let $p: E\to B$ be a covering map. If $B$ is compact and $p^{-1}(b)$ is finite, then $E$ is compact.
69367
covering map with finite fibres and preimage of a compact set
45249
Pseudocompactness does not imply compactness
73154
Compact subset in colimit of spaces
63529
How to show that this set is compact in $\ell^2$
28406
composition of certain covering maps
11114
Is a closed subset of a compact set (which is a subset of a metric space $M$) compact?
19566
Continuous images of compact sets are compact
116663
If f is a continuous map from X to Y with X limit point compact, does it follow that f(X) is limit point compact?
95993
Isn't every subset of a compact space compact?
29474
Compactness of $\operatorname{Spec}(A)$
29744
Compactness and axiomatisability
139702
Is $O_{C_p}$ and ${O_{C_p}}^\times$ a profinite group or compact?
128457
Show that $T$ is a compact operator
50611
Question about Stone-Čech compactification
47668
Show that $lim_{n \rightarrow \infty}m(O_n)=m(E)$ when $E$ is compact.
22464
Which of the following subsets of   $\mathbb{R}^2$ are compact
147237
If $A$ and $B$ are compact subsets of $\mathbb R$, then so is $\frac{A}B$.