query: Why is $\emptyset$ called both open and closed
positive_passages.docid: 148213
positive_passages.text: Given a topological space $X$, why are both $X$ and $\emptyset$ open and closed?
negative_passages.docid: 62542
negative_passages.text: Why is the empty set considered an interval?
negative_passages.docid: 3072
negative_passages.text: If the empty set is a subset of every set, why isn't $\{\emptyset,\{a\}\}=\{\{a\}\}$?
negative_passages.docid: 148507
negative_passages.text: Why an open set in $R^n$ might not be written as countable union of disjoint open intervals?
negative_passages.docid: 42494
negative_passages.text: The boundary is a closed set
negative_passages.docid: 73130
negative_passages.text: A simple question about open set
negative_passages.docid: 97951
negative_passages.text: Is the void set (∅) a proper subset of every set?
negative_passages.docid: 65768
negative_passages.text: What is the cardinality of the set of the empty set?
negative_passages.docid: 99678
negative_passages.text: Is a sphere a closed set?
negative_passages.docid: 18828
negative_passages.text: Base and empty set of a topology
negative_passages.docid: 118824
negative_passages.text: What is the complement of empty set?
negative_passages.docid: 123897
negative_passages.text: Sum of two open sets is open?
negative_passages.docid: 46698
negative_passages.text: Showing a set is closed under inverses
negative_passages.docid: 76162
negative_passages.text: Does Scala's pattern matching violate the Open/Closed Principle?
negative_passages.docid: 144731
negative_passages.text: Disjoint closed sets in a second countable zero-dimensional space can be separated by a clopen set
negative_passages.docid: 152976
negative_passages.text: Real Analysis: open and closed sets
negative_passages.docid: 132692
negative_passages.text: Nonempty set mapped to $\emptyset$ and vice-versa