The definition of a complete metric space
44457
Why we define the completeness of a space by the converge of a Cauchy sequence rather than a normal sequence?
143674
Space of bounded functions is complete
53429
In a complete metric space with no isolated points, any countable intersection of open dense sets is uncountable?
144400
Are compact subsets of metric spaces closed and bounded?
82333
let $(X,d)$ be a metric space. How I can show that any finite subset of $X$ is closed.
116069
Is every metric space a subspace of some connected metric space?
124179
Proof that every metric space is normal
15480
Open set in a metric space is union of closed sets
31686
Every metric space can be isometrically embedded in a Banach space, so that it's a linearly independent set
126759
Unbounded continuous function on non-compact metric space
114061
Construct such $d$ that $(\mathbb{R} \setminus \mathbb{Z}, d)$ is complete metric space
90628
The metric spaces are Tychonoff spaces
118496
Why do we essentially need complete measure space?
98553
Infinite metric space has open set $U$ which is infinite and its complement is infinite
113688
Is Topological Space a Metric Space?
107701
Show that a connected metric space is $\epsilon$-chainable for $\epsilon>0$
67050
Every separable metric space has a countable base