query: Is the space $\mathbb N^ \mathbb N$ metrisable?
positive_passages.docid: 148516
positive_passages.text: Proof that $\omega^\omega$ is completely metrizable and second countable
negative_passages.docid: 144072
negative_passages.text: Are the spaces $\mathbb{H}^n$ and $\overline{\mathbb{R}}^n_+$ homeomorphic?
negative_passages.docid: 68490
negative_passages.text: For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$
negative_passages.docid: 981
negative_passages.text: If $n^c\in\mathbb N$ for every $n\in\mathbb N$, then $c$ is a non-negative integer?
negative_passages.docid: 24561
negative_passages.text: $\mathbb S_n$ as semidirect product
negative_passages.docid: 156671
negative_passages.text: Necessary and sufficient condition for $x^n - y^m$ to be irreducible in $\Bbb C[x,y]$
negative_passages.docid: 31990
negative_passages.text: Is $\{\frac{m}{10^n}\mid m,n\in\mathbb Z,\ n\geq 0\}$ dense in $\mathbb R$?
negative_passages.docid: 119648
negative_passages.text: For which $n$ and $k$ are there nontrivial homomorphisms from $S_n$ to $\mathbb{Z}/k\mathbb{Z}$?
negative_passages.docid: 6161
negative_passages.text: The cartesian product $\mathbb{N} \times \mathbb{N}$ is countable
negative_passages.docid: 63285
negative_passages.text: Prove that this space is not Banach
negative_passages.docid: 33207
negative_passages.text: Bases having countable subfamilies which are bases in second countable space
negative_passages.docid: 6523
negative_passages.text: Prove that the space has a countable dense subset
negative_passages.docid: 97878
negative_passages.text: Are there uncountably many surjections from $\mathbb N$ to $\mathbb N$?
negative_passages.docid: 21114
negative_passages.text: $S=\{(n,{1\over n}):n\in\mathbb{N}\}$ is closed in $X$?
negative_passages.docid: 83446
negative_passages.text: bijective continuous function on $\mathbb R^n$ not homeomorphism?
negative_passages.docid: 42883
negative_passages.text: Cross product in $\mathbb R^n$
negative_passages.docid: 124847
negative_passages.text: Is the set of surjective functions from $\mathbb{N}$ to $\mathbb{N}$ uncountable?