query: Open sets and intervals
positive_passages.docid: 21892
positive_passages.text: Any open subset of $\Bbb R$ is a countable union of disjoint open 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: 85225
negative_passages.text: The set of integers is not open or is open
negative_passages.docid: 152193
negative_passages.text: The intersection of a closure with an open set
negative_passages.docid: 73130
negative_passages.text: A simple question about open set
negative_passages.docid: 91736
negative_passages.text: Explicit homeomorphism between open and closed rational intervals?
negative_passages.docid: 3896
negative_passages.text: A closed set in $(A, \mathcal T_A)$ that is not closed in $(X, \mathcal T)$
negative_passages.docid: 129227
negative_passages.text: An example of neither open nor closed set
negative_passages.docid: 63701
negative_passages.text: An example of a regular function over an open set
negative_passages.docid: 125233
negative_passages.text: Why is an open interval not a compact set?
negative_passages.docid: 94825
negative_passages.text: Open set as a finite union of closed sets
negative_passages.docid: 156520
negative_passages.text: Intervals are connected and the only connected sets in $\mathbb{R}$
negative_passages.docid: 47992
negative_passages.text: Is there a function $f\colon\mathbb{R}\to\mathbb{R}$ such that every non-empty open interval is mapped onto $\mathbb{R}$?
negative_passages.docid: 84359
negative_passages.text: On Lebesgue Outer Measure of an interval
negative_passages.docid: 43535
negative_passages.text: show that the interval of the form $[0,a)$ or $(a, 1]$ is open set in metric subspace $[0,1]$ but not open in $\mathbb R^1$
negative_passages.docid: 73559
negative_passages.text: Map preserving intervals but discontinuous
negative_passages.docid: 153934
negative_passages.text: How to prove that a set R\Z is open