query: A set $E$ such that $E$ is dense in $[0,1]\times [0,1]$, and the intersection of $E$ and any line parallel to the axes has at most one point
positive_passages.docid: 64920
positive_passages.text: Boundary Question in $\mathbb{R}^{2}$ (Manifolds)
negative_passages.docid: 8557
negative_passages.text: Invertible Matrices are dense
negative_passages.docid: 4381
negative_passages.text: Proof that the set of irrational numbers is dense in reals
negative_passages.docid: 33734
negative_passages.text: Every closed subset $E\subseteq \mathbb{R}^n$ is the zero point set of a smooth function
negative_passages.docid: 157218
negative_passages.text: If $E\subseteq X$ is connected, $E\cap A\neq\emptyset$ and $E\cap(X\setminus A)\neq\emptyset$ then $E\cap\partial A\neq\emptyset$
negative_passages.docid: 84609
negative_passages.text: Unary intersection of the empty set
negative_passages.docid: 120599
negative_passages.text: Points of a Measure Zero Sets Covered by Intervals Infinitely Many Times
negative_passages.docid: 144362
negative_passages.text: The construction of a Vitali set
negative_passages.docid: 63413
negative_passages.text: For a set of positive measure there is an interval in which its density is high, $\mu(E\cap I)> \rho \mu(I)$
negative_passages.docid: 37206
negative_passages.text: $\mathbb{R}^n\times\{0\}$ has measure zero in $\mathbb{R}^{n+1}$
negative_passages.docid: 146204
negative_passages.text: Subsets sharing at most $i$ elements
negative_passages.docid: 36546
negative_passages.text: For an irrational number $a$ the fractional part of $na$ for $n\in\mathbb N$ is dense in $[0,1]$
negative_passages.docid: 33642
negative_passages.text: Finite dimensional subspace of $C([0,1])$
negative_passages.docid: 19289
negative_passages.text: complement of a set and its measure
negative_passages.docid: 21570
negative_passages.text: Intersection of a family of non-empty closed intervals
negative_passages.docid: 22558
negative_passages.text: Vitali-type set with given outer measure
negative_passages.docid: 3023
negative_passages.text: Construction of a Borel set with positive but not full measure in each interval