Show that $S=\mathbb R^2\setminus\{(a,b):a,b\in\mathbb Q\}$ is path connected.
14345
If $A\subset\mathbb{R^2}$ is countable, is $\mathbb{R^2}\setminus A$ path connected?
139064
Show by using logical connectives laws that $(P\to Q) \land (Q \to R) $ is equivalent to $(P \to R) \land [(P \iff Q) \lor (R \iff Q)]$
108394
Proof of that every interval is connected
104411
sum of two connected subset of $\mathbb{R}$
108909
Is the unit sphere in $\Bbb R^4$ path connected?
144383
The closure of a connected set in a topological space is connected
126192
Connected, locally connected, path-connected but not locally path-connected subspace of the plane
101712
Let $X$ be obtained by removing finitely many lines from $\mathbb{R}^3$. How do I prove $X$ is connected?
84654
The graph of xy = 1 is connected or not
109682
Proposed proof of: If $A \subset B \subset \bar{A}$ and $A$ is connected, then $B$ is connected
144266
set theory proof of $A\cap B = A \setminus(A\setminus B)$
138297
Let $G = GL_2\mathbb (R)$. Show that $T$ is a subgroup of $G$
36878
Prove that $\operatorname{SL}(n,\Bbb R)$ is connected.
31266
Proof of "the continuous image of a connected set is connected"
16517
Arcwise connected part of $\mathbb R^2$
23225
Union of connected subsets is connected if intersection is nonempty
152442
An annulus in $\mathbb R^2$ is path connected