Compact metric space: proof $\text{diam}(K)$
70106
diameter on a compact metric space
124179
Proof that every metric space is normal
31686
Every metric space can be isometrically embedded in a Banach space, so that it's a linearly independent set
143484
A separable locally compact metric space is compact iff all of its homeomorphic metric spaces are bounded
26794
Metrizability of Hausdorff continuous image of compact metric space
51227
Proving that given metric space is complete: $X := (0,\infty)$ and $d:=|\ln(x)-\ln(y)|$
35652
Every compact metric space is complete
28804
No. of possible dense subsets of a metric space
29303
Cartesian product of compact sets is compact
138607
Proof that a limit point compact metric space is compact.
123061
$X$ metric separable then $C(X)$ separable
49563
Cauchy nets in a metric space
129243
Is $C_{c}^{\infty}[a,b]$ a complete metric space?
72950
Book recommendation for Metric Spaces
15480
Open set in a metric space is union of closed sets
83159
Defining a metric space
148403
Compact space and Hausdorff space