query: Is there a sequence of unbounded closed intervals such that its intersection is empty?
positive_passages.docid: 21570
positive_passages.text: Intersection of a family of non-empty closed intervals
negative_passages.docid: 11586
negative_passages.text: Sequences of Real Numbers in a closed bounded interval
negative_passages.docid: 82628
negative_passages.text: Cardinality of a set of closed intervals
negative_passages.docid: 157753
negative_passages.text: Show that any set in a metric space can be written as the intersection of open sets
negative_passages.docid: 3649
negative_passages.text: Closed unit interval is connected proof
negative_passages.docid: 55729
negative_passages.text: Family of Closed/Open Nested Intervals
negative_passages.docid: 158155
negative_passages.text: Is set of isolated points of S closed?
negative_passages.docid: 108619
negative_passages.text: Proving Baire's theorem: The intersection of a sequence of dense open subsets of a complete metric space is nonempty
negative_passages.docid: 148638
negative_passages.text: Write $(0,1)$ as a countable union of disjoint open intervals
negative_passages.docid: 14219
negative_passages.text: Is the intersection of a closed set and a compact set always compact?
negative_passages.docid: 116806
negative_passages.text: Find the weak sequential closure of a set in $L^2(-\pi,\pi)$
negative_passages.docid: 127972
negative_passages.text: Can distance between two closed sets be zero?
negative_passages.docid: 69283
negative_passages.text: The limit points of an open interval (open set)
negative_passages.docid: 44623
negative_passages.text: Closed set as a countable intersection of open sets
negative_passages.docid: 128987
negative_passages.text: A collection of pairwise disjoint open intervals must be countable
negative_passages.docid: 47903
negative_passages.text: How to prove every closed interval in R is compact?
negative_passages.docid: 88028
negative_passages.text: Topology - closures of intervals with the order topology