Prove that there is a non-zero distance between any point outside an open set and any point in a closed-bounded subset (Complex Analysis)
2978
A and B disjoint, A compact, and B closed implies there is positive distance between both sets
12467
Why does this proof work: Closed unit ball in $C_0$ is not compact
77576
Using the triangle inequalities to prove a bound in the complex plane
70264
Prove that the inverse image of an open set is open
88535
Relation between the distance from a point to the resolvent set of a self-adjoint operator and the norm of a related operator
14896
Prove: the set of zeros of a continuous function is closed.
60053
Does the boundary of an open set have measure zero (in $\mathbb{R}^n$)?
132382
Showing a set is nowhere dense in $C([0,1])$
68255
Theorems in complex analysis.
110957
No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof?
12293
Let X be a T1 space, and show that X is normal if and only if each neighbourhood of a closed set F contains the closure of some neighbourhood of F
79531
Distance between sets with one closed set and one compact set
64748
analytic in open unit disk,corresponding to a bounded sequence and a bounded functional sequence
129081
Proof that convex open sets in $\mathbb{R}^n$ are homeomorphic?
32534
Prove that a set $S \subseteq \mathbb{R}$ is closed and bounded if and only if every sequence in $S$ has a sub sequence converging to a point of $S$.
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
92774
Prove that a linear subspace of $C([0,1])$ is closed