Question on completing proof separability in metric space implies countability
67050
Every separable metric space has a countable base
35573
A closed ball in a metric space is a closed set
107701
Show that a connected metric space is $\epsilon$-chainable for $\epsilon>0$
62479
A isometric map in metric space is surjective?
119105
If $(X,d)$ is a complete metric space and $A$ is closed then show that for $x \in X$ there exists an element $a_0 \in A$ such that $d(x,A)=d(x,a_0)$
13848
Showing that if a subset of a complete metric space is closed, it is also complete
82333
let $(X,d)$ be a metric space. How I can show that any finite subset of $X$ is closed.
36184
Countability of disjoint intervals
53429
In a complete metric space with no isolated points, any countable intersection of open dense sets is uncountable?
69528
Metrizability of quotient spaces of metric spaces
88904
Help with a proof. Countable sets.
129243
Is $C_{c}^{\infty}[a,b]$ a complete metric space?
108619
Proving Baire's theorem: The intersection of a sequence of dense open subsets of a complete metric space is nonempty
91991
How do I prove that two closed sets are separable?
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.
136094
$G_\delta$ singletons in compact Hausdorff and first countability
88185
Proof that a subspace $A$ of a complete metric space $X$ is complete iff $A$ is closed