A continuous surjection makes $m \geq n$.
110885
Does there exists a continuous surjection from $\mathbb{R}$ to $\mathbb{R}^2$?
16610
Surjectivity of a map from a space to itself
27265
Continuously differentiable map from $\mathbb{R}^{m+n}$ to $\mathbb{R}^n$
45792
Rigorous proof that surjectivity implies injectivity for finite sets
33330
Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$
84512
The preimage of continuous function on a closed set is closed.
17223
Continuity of an inverse function.
100465
Does there exist a continuous bijection from $(-1,1) \to (-1,1]$?
125682
Proof verification: the product of two continuous functions is continuous
44069
Proof that a continuous map to $S^n$ whose image is a proper subset of $S^n$ is null-homotopic
143174
property of continuous function
46748
If $g \circ f$ is surjective, show that $f$ does not have to be surjective?
148500
Understanding this theorem and how to go about proving it surjectivity?
143800
continuous map on $\mathbb{R}$ which is the identity on $\mathbb{Q}$ is the identity map, hence Aut$(\mathbb{R}/\mathbb{Q})= 1.$
134104
Is there a Cantor-Schroder-Bernstein statement about surjective maps?
122086
continuous function: preimage of closure of a set is closure of preimage
6023
Surjectivity of Composition of Surjective Functions