query: Set of rational number in (0,1) can not be expressed as intersection of countable collection of open sets
positive_passages.docid: 4518
positive_passages.text: How would one go about proving that the rationals are not the countable intersection of open sets?
negative_passages.docid: 5215
negative_passages.text: Can the principle of inclusion/exclusion be used to count elements in the intersection of a sequence of sets?
negative_passages.docid: 68994
negative_passages.text: Countable closed sets
negative_passages.docid: 133086
negative_passages.text: When Cantor's Intersection theorem won't work with closed sets
negative_passages.docid: 143586
negative_passages.text: Is $[0,1]$ a union of family of disjoint closed intervals?
negative_passages.docid: 129227
negative_passages.text: An example of neither open nor closed set
negative_passages.docid: 88904
negative_passages.text: Help with a proof. Countable sets.
negative_passages.docid: 23442
negative_passages.text: Cardinality of the union of infinite and countable sets
negative_passages.docid: 93606
negative_passages.text: Showing that $C[0,1]$ is not complete
negative_passages.docid: 75012
negative_passages.text: Additive group of rationals has no minimal generating set
negative_passages.docid: 34998
negative_passages.text: How to prove that $\mathbb{Q}$ ( the rationals) is a countable set
negative_passages.docid: 11959
negative_passages.text: What's wrong with this argument that $[0,1]$ is countable?
negative_passages.docid: 70048
negative_passages.text: In which topologies do open sets maintain open under countable or arbitrary intersection?
negative_passages.docid: 53429
negative_passages.text: In a complete metric space with no isolated points, any countable intersection of open dense sets is uncountable?
negative_passages.docid: 68139
negative_passages.text: Show that the set of polynomials with rational coefficients is countable.
negative_passages.docid: 132778
negative_passages.text: All distances are rational prove the set is countable
negative_passages.docid: 19297
negative_passages.text: Is the cofinite topology on an uncountable set first countable?