query: How is $\mathbb R^2\setminus \mathbb Q^2$ path connected?
positive_passages.docid: 15865
positive_passages.text: Show that $X = \{ (x,y) \in\mathbb{R}^2\mid x \in \mathbb{Q}\text{ or }y \in \mathbb{Q}\}$ is path connected.
negative_passages.docid: 10541
negative_passages.text: How to prove Mandelbrot set is simply connected?
negative_passages.docid: 155794
negative_passages.text: Are the complements of two homeomorphic compact, connected subsets of $\mathbb{R}^2$ homeomorphic?
negative_passages.docid: 88301
negative_passages.text: What are all of the connected subsets of $\mathbb{Q}$?
negative_passages.docid: 85713
negative_passages.text: Showing Parallelism is an equivalence relation in $\Bbb R ^2$
negative_passages.docid: 85332
negative_passages.text: Is $\mathbb{R}^4$ minus a line simply connected?
negative_passages.docid: 67088
negative_passages.text: Closure and pathwise connected
negative_passages.docid: 61816
negative_passages.text: Cut points and connected space
negative_passages.docid: 80524
negative_passages.text: Path-connected and locally connected space that is not locally path-connected
negative_passages.docid: 11000
negative_passages.text: Fundamental group of $\mathbb{R}^2 \setminus (\mathbb{Z} \times \{0\})$
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: 63442
negative_passages.text: Show that if $U$ is an open connected subspace of $\mathbb{R}^2$, then $U$ is path connected
negative_passages.docid: 116538
negative_passages.text: Proof of Connected Diagrams
negative_passages.docid: 93986
negative_passages.text: Connectivity, Path Connectivity and Differentiability
negative_passages.docid: 46917
negative_passages.text: How to prove that $GL(n,\mathbb R)$ is not connected subset and open subset of$M_n (\mathbb{R})$
negative_passages.docid: 42883
negative_passages.text: Cross product in $\mathbb R^n$
negative_passages.docid: 86015
negative_passages.text: $\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$