Existence of unique fixed point in compact Metric space
54222
Prove the map has a fixed point
97914
Contractive mapping on compact space
156850
Fix-Point Theorem Proof.
149999
fixed point of a continuous map on a projective space
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.
126944
Metric spaces problem
118508
Is the axiom of choice needed in proving that metric spaces in which every infinite subset has a limit point are compact?
72950
Book recommendation for Metric Spaces
69528
Metrizability of quotient spaces of metric spaces
142414
Generalization of metric spaces?
35573
A closed ball in a metric space is a closed set
62479
A isometric map in metric space is surjective?
61884
If $T^n$ is $q$-contractive, $T$ exactly has one fixed point
152057
Let $(X,d)$ be a compact metric space. Let $f: X \to X$ be such that $d(f(x),f(y)) = d(x,y)$ for all $x,y \in X$. Show that $f $ is onto (surjective).
149390
Fixed point of a Function (monotonically increasing)
45581
Is the distance function in a metric space (uniformly) continuous?
31686
Every metric space can be isometrically embedded in a Banach space, so that it's a linearly independent set