query: Show that $\mathbb{Q}$ is not open.
positive_passages.docid: 105445
positive_passages.text: Are the rationals a closed or open set in $\mathbb{R}$?
negative_passages.docid: 3896
negative_passages.text: A closed set in $(A, \mathcal T_A)$ that is not closed in $(X, \mathcal T)$
negative_passages.docid: 113892
negative_passages.text: Show $A \in \cal F$ exists, such that $\mathbb P(A)=1$ and $\mathbb Q(A)=0$.
negative_passages.docid: 11405
negative_passages.text: If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
negative_passages.docid: 74330
negative_passages.text: $\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
negative_passages.docid: 157597
negative_passages.text: Homeomorphism between $\mathbb{Q}$ and $\mathbb{Q}(>0)$, and $\mathbb{Q}(\ge 0)$
negative_passages.docid: 85225
negative_passages.text: The set of integers is not open or is open
negative_passages.docid: 27188
negative_passages.text: Bijection between $\mathbb{R}$ and $\mathbb{R}/\mathbb{Q}$
negative_passages.docid: 85586
negative_passages.text: Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$
negative_passages.docid: 126927
negative_passages.text: $\mathbb Q$ is not the direct product of two non-trivial groups.
negative_passages.docid: 133312
negative_passages.text: Are these polynomials irreducible in $\mathbb{Q}[x]$?
negative_passages.docid: 66531
negative_passages.text: $\|h(x)-h(y)\|\geq 3\|x-y\|$ prove that image of open is open
negative_passages.docid: 55050
negative_passages.text: How to show that $\mathbb{Q}(i,\sqrt[4]{1+i} )$ is not contained in any cyclotomic extension of $\mathbb{Q}(i)$?
negative_passages.docid: 110217
negative_passages.text: $GL(n,K)$ is open in $M(n,K)$
negative_passages.docid: 90055
negative_passages.text: Show that $\mathcal P(x)\notin x$
negative_passages.docid: 128766
negative_passages.text: Show that the set of functions $\mathbb{N}\to\{0,1\}$ is not countable
negative_passages.docid: 21599
negative_passages.text: $(0,1)$ is an open subset of $\mathbb{R}$ but not of $\mathbb{R}^2$, when we think of $\mathbb{R}$ as the x-axis in $\mathbb{R}^2$. Prove this.