A method to choose a point from a nonempty closed set to avoid the use of $\mathsf{AC}$
35156
Constructing a choice function in a complete & separable metric space
76764
Find two closed subsets or real numbers such that $d(A,B)=0$ but $A\cap B=\varnothing$
84686
Geometric Description Of a Set In The Complex Plane
128482
The set of subsequential limits is closed
111096
How can I select a point without selecting its reflected side
77548
Given an arbitrary infinite set $S$, how to construct an injection $\mathbb{N} \to S$ with the Axiom of Choice?
79531
Distance between sets with one closed set and one compact set
34964
Recursive representation of closed sets in Baire Space ($\Sigma^1_1$)
144181
Given an arbitrary set $X$, can one always find an element outside $X$?
124732
Finding a nonempty subset that is not a subgroup
53132
A convex subset of a set has 'smaller' boundary than the set?
136108
Arbitrary intersection of closed, connected subsets of a compact space connected?
82628
Cardinality of a set of closed intervals
41365
Choice function for collection of arbitrary finite sets. AC required?
128844
An empty intersection of decreasing sequence of closed sets
94231
Prove that a non-empty closed convex $S$ has an extreme point iff it does not contain any line
116806
Find the weak sequential closure of a set in $L^2(-\pi,\pi)$