Existence of $f(x)=-x$ for null homotopic maps on $S^n$.
130872
Map $f: S^n \to S^n$ that extends over $D^{n+1}$ must identify a pair of antipodal points
69367
covering map with finite fibres and preimage of a compact set
72115
Why isn't there a continuously differentiable surjection from $I \to I \times I$?
120100
Hairy Ball Theorem: homotopy from the identity to the antipodal map
2717
Help proving existence of an specific $x_0$ for which $f''(x_0)=0$
50649
On the existence of a continuous bijection $f\colon [0,1]\to [0,1]\times [0,1]$
29582
Continuous mapping $f: [0,1]\rightarrow (0,1)$ CSIR December $2013$
26687
Show that $f$ maps the unit circle to itself
52729
Homotopic maps $(X, A) \to (Y, B)$ induce homotopic maps $X/A \to X/B$
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
64084
Existence of a simple closed curve which is not null-homotopic
12104
How to prove this result involving the quotient maps and connectedness?
67291
Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$
88311
Linear functional f(v)=0 imply v=0
11319
Is $M=\{(x,|x|): x \in (-1, 1)\}$ not a differentiable manifold?
110202
Is the image of a null set under a differentiable map always null?
149248
Pushforward of inverse map at the identity?