query: Countable open cover $\{U_i\}$ with each $U_i$ second countable
positive_passages.docid: 16649
positive_passages.text: Topological space with countable open cover $\{U_\alpha\} $ with each $U_\alpha$ second-countable, is second countable
negative_passages.docid: 9021
negative_passages.text: An infinite subset of a countable set is countable
negative_passages.docid: 55717
negative_passages.text: cardinality of the Borel $\sigma$-algebra of a second countable space
negative_passages.docid: 130361
negative_passages.text: Basis for a topology with a countable number of sets
negative_passages.docid: 62793
negative_passages.text: $\mathbb{R}$ with the lower limit topology is not second-countable
negative_passages.docid: 118595
negative_passages.text: Proving that a set is countable by finding a bijection
negative_passages.docid: 55374
negative_passages.text: Cover of (0,1) with no finite subcover & Open sets of compact function spaces
negative_passages.docid: 27937
negative_passages.text: Cartesian Product of Two Countable Sets is Countable
negative_passages.docid: 84936
negative_passages.text: The set of all finite sequences of members of a countable set is also countable
negative_passages.docid: 70143
negative_passages.text: Mutually exclusive countable subsets of a countable set
negative_passages.docid: 138768
negative_passages.text: Showing that the family of Borel sets is countably generated
negative_passages.docid: 3708
negative_passages.text: How can I prove that compact subset iff sequentially compact in second countable topological spaces?
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: 80096
negative_passages.text: Prove that the union of countably many countable sets is countable.
negative_passages.docid: 104550
negative_passages.text: Countable union of countable sets(ZF)
negative_passages.docid: 39956
negative_passages.text: Union of uncountable cardinals
negative_passages.docid: 66301
negative_passages.text: The cardinality of the set of countably infinite subsets of an infinite set