query: The first countable space
positive_passages.docid: 19297
positive_passages.text: Is the cofinite topology on an uncountable set first countable?
negative_passages.docid: 23837
negative_passages.text: Why is $\mathbb{R}/{\sim}$ not first countable at $[0]$, where $x \sim y \Leftrightarrow x = y\text{ or }x,y \in \mathbb{Z}$?
negative_passages.docid: 99478
negative_passages.text: countably infinite union of countably infinite sets is countable
negative_passages.docid: 87983
negative_passages.text: Examples of Separable Spaces that are not Second-Countable
negative_passages.docid: 132778
negative_passages.text: All distances are rational prove the set is countable
negative_passages.docid: 105358
negative_passages.text: In a second countable space any base has a countable subset that is still a base
negative_passages.docid: 92005
negative_passages.text: Existence of compact/complete metric on countable set
negative_passages.docid: 122506
negative_passages.text: Relation on countable sets
negative_passages.docid: 74877
negative_passages.text: Every metric space with a countable base is separable
negative_passages.docid: 104550
negative_passages.text: Countable union of countable sets(ZF)
negative_passages.docid: 95747
negative_passages.text: Number of countable subsets of $\mathbb{R}$
negative_passages.docid: 103769
negative_passages.text: The Cartesian product of a finite number of countable sets is countable
negative_passages.docid: 4111
negative_passages.text: Outer measure is countably subadditive
negative_passages.docid: 48174
negative_passages.text: Are countable topological spaces second-countable?
negative_passages.docid: 106606
negative_passages.text: How to prove that compact subspaces of the Sorgenfrey line are countable?
negative_passages.docid: 7402
negative_passages.text: Showing a compact metric space has a countable dense subset
negative_passages.docid: 134844
negative_passages.text: Summablity and countability