For a compact metric space $X ,f: X \rightarrow X $ s.t $ d(x,y)\leq d(f(x),f(y))$ is surjective
37308
Let $f:K\to K$ with $\|f(x)-f(y)\|\geq ||x-y||$ for all $x,y$. Show that equality holds and that $f$ is surjective.
60655
$\ker T\subset \ker S\Rightarrow S=rT$ when $S$ and $T$ are linear functionals
69528
Metrizability of quotient spaces of metric spaces
99645
Metrizable topological space $X$ with every admissible metric complete then $X$ is compact
104757
If $f \circ g$ is surjective, then f is surjective
42638
Showing that a function $f$ has a unique fixed point in a metric space.
95831
Compactness and sequential compactness in metric spaces
116732
Proving that a continuous map 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 $d(x,A)=d(x,a_0)$
63146
Proof of properties of injective and surjective functions.
114061
Construct such $d$ that $(\mathbb{R} \setminus \mathbb{Z}, d)$ is complete metric space
124179
Proof that every metric space is normal
99816
Existence of Topologically Transitive Maps on nice Metric Spaces
148500
Understanding this theorem and how to go about proving it surjectivity?
46970
If $X$ is compact and $T:X \to Y$ continuous and bijective, show that $T$ is homeomorphism.
27517
Isometry in compact metric spaces
11383
Disjoint compact sets in a Hausdorff space can be separated