query: why $H^\mathrm{o}=K^\mathrm{o}=\emptyset$
positive_passages.docid: 17525
positive_passages.text: Why the interior of $\mathbb{Q}$ in $\mathbb{R}$ is empty?
negative_passages.docid: 94571
negative_passages.text: How can we prove that $N_G(H)=H$ implies $N_{f(G)}(f(H))=f(H)$
negative_passages.docid: 13282
negative_passages.text: In the category $\mathbf{Set}$ is "the product of an empty set of sets a one-element set"?
negative_passages.docid: 123498
negative_passages.text: Is "empty set" an element of a set?
negative_passages.docid: 858
negative_passages.text: Is $\{\emptyset\}$ a subset of $\{\{\emptyset\}\}$?
negative_passages.docid: 35631
negative_passages.text: $H_0(X,A) = 0 \iff A \cap X_i \neq \emptyset \forall $ path-components $X_i$
negative_passages.docid: 91222
negative_passages.text: Isomorphism between $\mathfrak o(4,\mathbb R)$ and $\mathfrak o (3,\mathbb R) \oplus\mathfrak o (3,\mathbb R) $
negative_passages.docid: 105910
negative_passages.text: How to prove that $[G:xHx^{-1}] = [G:H]$ given $H \le G$?
negative_passages.docid: 128256
negative_passages.text: How to prove $H_1(\mathbb{C}/\Lambda, \mathbb{Z})$ to the lattice $\Lambda$ ,$\gamma \mapsto \int_\gamma dz$ is well defined?
negative_passages.docid: 125008
negative_passages.text: Define a bijection between $Z^{X \cup Y}$ and $Z^X \times Z^Y$, where $X, Y \in \mathcal{P}(\Omega) $ and $X \cap Y = \emptyset$
negative_passages.docid: 79367
negative_passages.text: Understanding the difference between two theorems related to $|G\,:\,K|=|H\,:\,K|\cdot|G\,:\,H|$.
negative_passages.docid: 127000
negative_passages.text: When does $V = \ker(f) \oplus \operatorname{im}(f)$?
negative_passages.docid: 27436
negative_passages.text: Does $G\cong G/H$ imply that $H$ is trivial?
negative_passages.docid: 52461
negative_passages.text: Why does $(g^b \bmod m)^a \bmod m = (g^a \bmod m)^b \bmod m$?
negative_passages.docid: 120495
negative_passages.text: Does this correctly interpret the "$\cong$" between groups as "$=$" between sets?
negative_passages.docid: 65549
negative_passages.text: What is the cartesian product of an empty set of sets?
negative_passages.docid: 65768
negative_passages.text: What is the cardinality of the set of the empty set?