Proving $\mathbb R^2 \setminus \mathbb Q^2$ is connected
19754
$\mathbb{R}$ \ $\mathbb{Q}$ and $\mathbb{R}^2\setminus\mathbb{Q}^2$ disconnected?
125164
How to prove the existence of $b$ in $Q$ such that $a<b^2<c$ in $Q$?
35069
Connectedness of the boundary
5132
Given $A\cap \overline{B}\neq \emptyset$, prove $A\cup B$ connected.
1453
Prove that the graph is connected
123742
Proving connectedness of the $n$-sphere
105666
What's an easy way to show that $GL(n,\mathbb C)$ is connected?
101712
Let $X$ be obtained by removing finitely many lines from $\mathbb{R}^3$. How do I prove $X$ is connected?
108394
Proof of that every interval is connected
115272
Showing that projections $\mathbb{R}^2 \to \mathbb{R}$ are not closed
92740
prove that $\mathbb{Q}^n$is dense subset of $\mathbb{R^n}$
114198
Showing that $y$ is irreducible in $\mathbb R[x,y]/(x^2+y^2-1)$.
144266
set theory proof of $A\cap B = A \setminus(A\setminus B)$
105141
$\mathbb R[x]/\langle x^2+1\rangle\simeq\mathbb C$ and $\mathbb R[x]/\langle x^2+1\rangle$ contains a zero of $x^2+1$
39114
Prove that a set in $\mathbb R^3$ is not an algebraic set
88051
$\mathbb R = X^2$ as a Cartesian product
12104
How to prove this result involving the quotient maps and connectedness?