If $f,g:(X,A)\to (Y,B)$ are homotopic functions under a homotopy $H:X\times [0,1]\to Y$ then $f_*=g_*:H_n(X,A)\to H_n(Y,B)$.
52729
Homotopic maps $(X, A) \to (Y, B)$ induce homotopic maps $X/A \to X/B$
22995
Let f:G to H be 1-1 homomorphism show that order of f(a) divides the order of G.
86105
Can $\{(f(t),g(t)) \mid t\in [a,b]\}$ cover the entire square $[0,1] \times [0,1]$ ?
90649
Consider $f(x)=mx$ and $g(x) =bx$ in which $m>0$ and $b>0$. Does there exist any homeomorphism $h$ such that $h \circ f$ = $g \circ h$
7890
Prove the map $\Phi:G\to\operatorname{Aut}G$ with $g\mapsto (x\mapsto g^{-1}xg)$ is an homomorphism.
62454
Let $f : G → G_1$ be a surjective homomorphism (also called epimorphism) from $G$ to another group $G_1$. Prove that $f(Z(G)) \subseteq Z(G_1)$.
148668
How to show $A\times (B\cup C) = (A\times B)\cup (A\times C)$
84143
Given any function $g(x): \mathbb{R} \rightarrow \mathbb{R}$, find a function $f(x)$ such that $f(f(x)) = g(x)$.
116866
$A\times B$ connected component implies $A,B$ connect components
409
functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$
41477
Prove $f(S \cap T) \subseteq f(S) \cap f(T)$
53695
explicit formula for contraction of conus of homotopy equivalence
39090
Finding functions such that $f(g(x)) = f(x)g(x)$
20692
Homotopy groups of a wedge sum
107659
Let $f:A \to B$ and $g:B\to A$ be arbitrary functions.
53551
$f(A\cap B)=f(A)\cap f(B)$ $\iff$ $f$ is injective.
56364
Confusion about Homotopy Type Theory terminology