query: Is the subset $T=\{(x,y):x\notin \mathbb{Q} \text{ or } y \notin \mathbb{Q}\}$ connected?
positive_passages.docid: 16517
positive_passages.text: Arcwise connected part of $\mathbb R^2$
negative_passages.docid: 112731
negative_passages.text: If $Y$ is connected, why is $A\cup Y$ connected in this case?
negative_passages.docid: 35305
negative_passages.text: Why is $\mathbb{R}^2$ not a subset and /or a subspace of $\mathbb{R}^3$?
negative_passages.docid: 3148
negative_passages.text: True or false: {{∅}} ⊂ {∅,{∅}}
negative_passages.docid: 146364
negative_passages.text: $X$ is connected iff $\forall A\subset X,$ $\partial A\neq\emptyset$
negative_passages.docid: 74330
negative_passages.text: $\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
negative_passages.docid: 58285
negative_passages.text: Is it true that if $X$ is connected, then for every nonempty proper subset $A$ of $X$, we have $\mathbf{Bd} \ne \emptyset$
negative_passages.docid: 80827
negative_passages.text: Let $A$ be a nonempty subset of $\mathbb{R}$. Prove...
negative_passages.docid: 39746
negative_passages.text: How to prove that given set is a connected subset of the space of matrices?
negative_passages.docid: 45485
negative_passages.text: Dimension of a subset
negative_passages.docid: 15487
negative_passages.text: Continuous function from a connected set?
negative_passages.docid: 122271
negative_passages.text: A subset of a transitive set is transitive
negative_passages.docid: 116378
negative_passages.text: Nonhomeomorphic subsets of the plane
negative_passages.docid: 19754
negative_passages.text: $\mathbb{R}$ \ $\mathbb{Q}$ and $\mathbb{R}^2\setminus\mathbb{Q}^2$ disconnected?
negative_passages.docid: 42213
negative_passages.text: Computing $\text{Gal}(\mathbb{Q}^{ab}/\mathbb{Q})$
negative_passages.docid: 50645
negative_passages.text: Is the following set (path) connected?
negative_passages.docid: 858
negative_passages.text: Is $\{\emptyset\}$ a subset of $\{\{\emptyset\}\}$?