How to find an open cover of X which does not admit a finite subcover?
59275
If $X$ is an infinite set, then $X$ with the discrete topology is not compact
124732
Finding a nonempty subset that is not a subgroup
121135
Why don't we use closed covers to define compactness of metric space?
73458
Double cover of $GL(n,\mathbb{C})$.
43024
Well-ordered sets, properties of an element that is not largest in the set
127900
Interior of closure of open set in topological space
158523
Topology: Proof that a finitely generated cone is closed
4518
How would one go about proving that the rationals are not the countable intersection of open sets?
64261
example of not surjective isometry on a bounded not closed set.
78085
A non orientable closed surface cannot be embedded into $\mathbb{R}^3$
15645
Is convex open set in $\mathbb{R}^n$ is regular?
133152
(X,d) be a compact metric space. For every open cover, show there exists ε > 0 such that ∀𝑥 ∈ X, B(x,ε) is contained in some member of the cover.
122463
How to show the that a set $A$ nowhere dense is equivalent to the complement of $A$ containing a dense open set?
30022
Why use the double cover instead of the universal cover of $SO(2)$?
112727
Surfaces in $\mathbb P^3$ not containing any line
32923
Homotopy equivalence of universal cover
32759
Open neighborhood of the identity with no proper subgroup.