Consider $f(x) = 2x$ and $g(x)=4x$. Is there any homeomorphism $h:\mathbb{R}\rightarrow \mathbb{R}$ such that $h\circ f=g\circ h$
90649
Consider $f(x)=mx$ and $g(x) =bx$ in which $m>0$ and $b>0$. Does there exist any homeomorphism $h$ such that $h \circ f$ = $g \circ h$
70912
If $g\circ f$ is injective and $f$ is surjective then $g$ is injective
46970
If $X$ is compact and $T:X \to Y$ continuous and bijective, show that $T$ is homeomorphism.
78698
Prove if $f$ has a right inverse function: $f\circ g=id_x$ $\iff$ $f$ is onto $Y$
81264
Is $[0, 1) \times (0, 1)$ homeomorphic to $(0, 1) × (0, 1)$?
53425
Prove that there exists a Borel measurable function $h: \mathbb R \to \mathbb R$ such that $g= h\circ f$.
89514
Show that if $g \circ f$ is injective, then so is $f$.
51695
Finding all homomorphisms between $\mathbb{Z}/m\mathbb{Z}$ and $\mathbb{Z}/n\mathbb{Z}$
143140
When are quotients of homeomorphic spaces homeomorphic?
20547
Homeomorphism that maps given points to given points
63845
Diffeomorphism $f:U\to V$ then $Df:\mathbb{R^n}\to\mathbb{R^m}$ will be linear isomorphism hence $n=m$
18334
Equivalence between CH and existence of certain sets in $\mathbb{R}^2$
62454
Let $f : G → G_1$ be a surjective homomorphism (also called epimorphism) from $G$ to another group $G_1$. Prove that $f(Z(G)) \subseteq Z(G_1)$.
30178
Homeomorphism $(\mathbb{CP}^1)^m/S_m \overset{\sim}{\to} \mathbb{CP}^m$?
105910
How to prove that $[G:xHx^{-1}] = [G:H]$ given $H \le G$?
91878
Homeomorphism of the Disk
82458
Homeomorphism between the unit disc and the unit square