query: Only trivial sets are always open
positive_passages.docid: 152465
positive_passages.text: Find the intersection of all $T_2$ topologies on an infinite set $X$
negative_passages.docid: 91237
negative_passages.text: Every infinite set contains a countable subset
negative_passages.docid: 136106
negative_passages.text: Is every open subset of $ \mathbb{R} $ uncountable?
negative_passages.docid: 36721
negative_passages.text: Is "The empty set is a subset of any set" a convention?
negative_passages.docid: 138202
negative_passages.text: Every open set in $\mathbb{R}$ is a countable union of closed sets
negative_passages.docid: 58594
negative_passages.text: Is the empty set a subset of itself?
negative_passages.docid: 15438
negative_passages.text: do all uncountable sets have same cardinality as real numbers?
negative_passages.docid: 4213
negative_passages.text: The set that only contains itself
negative_passages.docid: 26008
negative_passages.text: Why there is a unique empty set?
negative_passages.docid: 34099
negative_passages.text: Proving that the empty set is unique
negative_passages.docid: 99064
negative_passages.text: Uncountable set with exactly one limit point
negative_passages.docid: 147136
negative_passages.text: Subset of a countable set is itself countable
negative_passages.docid: 62542
negative_passages.text: Why is the empty set considered an interval?
negative_passages.docid: 73130
negative_passages.text: A simple question about open set
negative_passages.docid: 50506
negative_passages.text: What concept does an open set axiomatise?
negative_passages.docid: 33064
negative_passages.text: Powerset of set with empty sets
negative_passages.docid: 123897
negative_passages.text: Sum of two open sets is open?