query: Show that $X = \{ (x,y) \in\mathbb{R}^2\mid x \in \mathbb{Q}\text{ or }y \in \mathbb{Q}\}$ is path connected.
positive_passages.docid: 19754
positive_passages.text: $\mathbb{R}$ \ $\mathbb{Q}$ and $\mathbb{R}^2\setminus\mathbb{Q}^2$ disconnected?
negative_passages.docid: 143831
negative_passages.text: Showing $\mathbb{Q}$ is homeomorphic to $\mathbb{Q}^2$
negative_passages.docid: 26919
negative_passages.text: Intersection of Connected Sets
negative_passages.docid: 135783
negative_passages.text: Let $T$ and $T^{'}$ be topologies on set $X$ such that $T \leq T^{'}$. If $(X,T^{'})$ is path-connected, is $(X,T)$ path connected?
negative_passages.docid: 129943
negative_passages.text: Torsion on $\pi_1(X)$, $X$ connected and open in $\mathbb{R}^n$
negative_passages.docid: 34177
negative_passages.text: Prove that $\mathbb{R}^2\setminus\mathbb{Q}^2$ is connected without path connectedness
negative_passages.docid: 93623
negative_passages.text: Showing that every connected open set in a locally path connected space is path connected
negative_passages.docid: 70193
negative_passages.text: Show that the relation defined on an integral domain by "$x\sim y$" ("$x$ is associated with $y$") is a relation of equivalence.
negative_passages.docid: 33822
negative_passages.text: Is there a monoid structure on the set of paths of a graph?
negative_passages.docid: 156443
negative_passages.text: if $x$ and $y$ commute with $[x y]$, then $[x y]$ is nilpotent
negative_passages.docid: 1932
negative_passages.text: How to show this equality of $\rho(X,Y)$
negative_passages.docid: 155579
negative_passages.text: Show that $End_A(A)$ = {$r_a$ | $a ∈ A$}
negative_passages.docid: 116866
negative_passages.text: $A\times B$ connected component implies $A,B$ connect components
negative_passages.docid: 105666
negative_passages.text: What's an easy way to show that $GL(n,\mathbb C)$ is connected?
negative_passages.docid: 55902
negative_passages.text: Show $R[x]/(x)\cong R$
negative_passages.docid: 14345
negative_passages.text: If $A\subset\mathbb{R^2}$ is countable, is $\mathbb{R^2}\setminus A$ path connected?
negative_passages.docid: 36878
negative_passages.text: Prove that $\operatorname{SL}(n,\Bbb R)$ is connected.