If a mapping $f:X \rightarrow S^4$ is not surjective, then it must be null-homotopic?
44069
Proof that a continuous map to $S^n$ whose image is a proper subset of $S^n$ is null-homotopic
60655
$\ker T\subset \ker S\Rightarrow S=rT$ when $S$ and $T$ are linear functionals
62479
A isometric map in metric space is surjective?
108408
Example of quotient mapping that is not open
116732
Proving that a continuous map is surjective
2348
Show that the sphere, S, and $\mathbb{R}^2$ is not homeomorphic
39453
How do I prove that $S^n$ is homeomorphic to $S^m \Rightarrow m=n$?
94165
Why is a map to a smaller dimensional space not injective?
110202
Is the image of a null set under a differentiable map always null?
11319
Is $M=\{(x,|x|): x \in (-1, 1)\}$ not a differentiable manifold?
78963
Homotopy lifting property of $\mathbb{R} \to S^1$ in Hatcher
85032
$Q(\mathbb{Z}[t]) / \mathbb{Z}[t]$ is not injective
151354
Why are there no non-trivial regular maps $\mathbb{P}^n \to \mathbb{P}^m$ when $n > m$?
121995
Hilbert's Nullstellensatz implies $I(Z(I)) = \sqrt{I}$
21391
Proving Functions are Surjective
35953
Prove that a function is not injective
6023
Surjectivity of Composition of Surjective Functions