Do we need the Axiome of Choice in proving a Sequentially Compact Metric Space is Totally Bounded?
58189
Bolzano-Weierstrass Theorem Proof Abbott (Ax. of Choice)
49563
Cauchy nets in a metric space
40682
What's going on with "compact implies sequentially compact"?
107701
Show that a connected metric space is $\epsilon$-chainable for $\epsilon>0$
146967
Understanding equivalent metric spaces
84004
Prove there is no contraction mapping from compact metric space onto itself
34674
Does the proof of Bolzano-Weierstrass theorem require axiom of choice?
97148
Does bounded variation imply boundedness
154578
Proving there is a sequence convergent to a limit point of a set without axiom of countable choice?
108619
Proving Baire's theorem: The intersection of a sequence of dense open subsets of a complete metric space is nonempty
29744
Compactness and axiomatisability
99645
Metrizable topological space $X$ with every admissible metric complete then $X$ is compact
124179
Proof that every metric space is normal
29836
Prove: Convergent sequences are bounded
130877
Boundedness and Cauchy Sequence: Is a bounded sequence such that $\lim(a_{n+1}-a_n)=0$ necessarily Cauchy?
109926
Axiom of Regularity and infinite sequences
88099
Not $\sigma$-compact set without axiom of choice