Prove that $S^1{\setminus\{(1,0)\}}$ is homeomorphic to $]0,1[$
60485
Show that $S^1 - \lbrace (1,0)\rbrace$ is homeomorphic to the open interval $(0,1)$
15175
When does a Möbius transformation map $\Im(z)>0$ to itself?
39455
Prove that $(X\times Y)\setminus (A\times B)$ is connected
82814
Homework question on whether two quotient spaces are homeomorphic
157002
Connected compact covering space of torus is homeomorphic to $S^1\times S^1$
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
68567
Prove that every complex number with modulus 1 and is not -1, has this property
86535
Prove quotient of two $N(0,1)$ is $\text{Cauchy}(0,1)$
16774
If $x,y,z\in\mathbb R\setminus \{1\}$ and $xyz=1$, prove that $\frac{x^2}{(x-1)^2}+\frac{y^2}{(y-1)^2}+\frac{z^2}{(z-1)^2}\ge 1$.
157597
Homeomorphism between $\mathbb{Q}$ and $\mathbb{Q}(>0)$, and $\mathbb{Q}(\ge 0)$
129081
Proof that convex open sets in $\mathbb{R}^n$ are homeomorphic?
52135
Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$
13993
Can we prove $ℝ^n ∖ \{\text{straight line}\}$ and $ℝ^n ∖ \text{\{an axis\}}$ homeomorphic by proving their complements homeomorphic?
143140
When are quotients of homeomorphic spaces homeomorphic?
86537
Prove that an open interval and a closed interval are not homeomorphic
107076
Prove $S^1$ is not homeomorphic to $S^2$ using connectedness
30178
Homeomorphism $(\mathbb{CP}^1)^m/S_m \overset{\sim}{\to} \mathbb{CP}^m$?