query: Density of $H^1_0(\mathbb{R}^n)$ in $H^1(\mathbb{R}^n)$
positive_passages.docid: 158011
positive_passages.text: $C_c^{\infty}(\mathbb R^n)$ is dense in $W^{k,p}(\mathbb R^n)$
negative_passages.docid: 111898
negative_passages.text: Is $\{ (e^{2\pi i a n},e^{2\pi i b n }) : n \in \mathbb{Z} \}$ dense in the torus, where $a,b$ irrationals such that $a/b$ irrational?
negative_passages.docid: 134065
negative_passages.text: A question about an $n$-dimensional subspace of $\mathbb{F}^{S}$.
negative_passages.docid: 63836
negative_passages.text: Show there exists $g:(0,1)\to\mathbb{R}^2$ such that $h\circ g$ constant, $g$ continuously differentiable and $g$ injective
negative_passages.docid: 55019
negative_passages.text: Lebesgue density theorem in the line
negative_passages.docid: 12212
negative_passages.text: Showing a certain subspace of Hilbert space is dense
negative_passages.docid: 121198
negative_passages.text: $W^{1,1}(\mathbb{R}^n)$ is not compactly embedded in $L^1(\mathbb{R}^n)$?
negative_passages.docid: 75829
negative_passages.text: Dimension of open subsets of $R^n$
negative_passages.docid: 20810
negative_passages.text: Boundary of Ball of radius R has zero measure
negative_passages.docid: 14048
negative_passages.text: Proof that the complement of zero-measure set on $[0,1]$ is dense in $[0,1]$
negative_passages.docid: 78915
negative_passages.text: Density of the set $S=\{m/2^n| n\in\mathbb{N}, m\in\mathbb{Z}\}$ on $\mathbb{R}$?
negative_passages.docid: 56433
negative_passages.text: Volume form on $(n-1)$-sphere $S^{n-1}$
negative_passages.docid: 36485
negative_passages.text: $H_n(X,A) \not \approx \tilde{H}_n(X/A)$
negative_passages.docid: 41651
negative_passages.text: Volume bounded by a sphere of radius $1$ in 4 dimensions
negative_passages.docid: 6270
negative_passages.text: Poincaré inequality for a subspace of $H^1(\Omega)$
negative_passages.docid: 113614
negative_passages.text: Approximating the density of $S\cap[a,b]$ using a Folner Sequence of $A$, where $S \subseteq A$?
negative_passages.docid: 22865
negative_passages.text: Sine function dense in $[-1,1]$