Is the unit circle homeomorphic to the unit square?
128301
Homeomorphism from square to unit circle
144521
Why does Möbius transformation $f(z)$ map the unit disk $|z|<1$ to itself?
67374
Is it true that $\mathbb{R}$ and $\mathbb{R}^2$ are isomorphic as abelian groups?
61204
Mapping that takes unit circle to unit circle
88155
Show that $[0, 1)\times[0, 1)$ is homeomorphic to $[0, 1]\times[0, 1)$ but not to $[0, 1]\times[0, 1]$.
18034
Is there an equivalence relation of which the quotient topology is homeomorphic to codomain of a quotient map?
127306
Is the group of units of a finite ring cyclic?
138383
group of units in a topological ring
58000
How can one show that a möbius transformation maps the unit circle to some axis?
88981
Explicit Homeomorphism from $\mathbb{R}^2$ to open disk
63731
Can we characterize the Möbius transformations that maps the unit disk into itself?
99884
Are $\mathbb{Q}_p$ and $\mathbb{Q}_q$ homeomorphic?
83493
Map an arbitrary triangle to the unit square
102729
Is there an equidissection of a unit square involving irrational coordinates?
140851
Precalculus unit circle with imaginary axis.
149971
Closed unit disk homeomorphic to $\mathbb{R}^2$?
41872
Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus\{(0,0)\}$