Is the axiom of choice necessary for "a set is open iff it is a neighborhood of all its points"?
73368
Does this proof that every open set in a metric space is a union of open balls use the axiom of choice?
81509
The cardinality of a countable union of countable sets, without the axiom of choice
85769
Do you need the Axiom of Choice to accept Cantor's Diagonal Proof?
24050
Characterization of the Closure of a Set
146188
Why does a proof of $\exists f: X\to Y$ injection $\iff \exists g: Y \to X$ surjection requires the axiom of choice?
126463
Can open sets and closed sets of $\mathbb{R}^n$ be homeomorphic?
16654
Unions and Intersections of Open Sets are Open
25256
When a lattice is a lattice of open sets of some topological space?
150385
The use of the Axiom of Choice in this proof of the sequence lemma
94825
Open set as a finite union of closed sets
157490
Statements equivalent to the Axiom of Choice
88099
Not $\sigma$-compact set without axiom of choice
70048
In which topologies do open sets maintain open under countable or arbitrary intersection?
78228
Hausdorff Maximal Principle and Axiom of Choice
136106
Is every open subset of $ \mathbb{R} $ uncountable?
99236
Interior of closure of an open set
152272
Can you explain the "Axiom of choice" in simple terms?