query: Subsets that contain the empty subset
positive_passages.docid: 16056
positive_passages.text: Is empty set element of every set if it is subset of every set?
negative_passages.docid: 39020
negative_passages.text: Why is empty set an open set?
negative_passages.docid: 82315
negative_passages.text: is an empty set an element of {empty set}
negative_passages.docid: 81351
negative_passages.text: Polish space in which the interior of each compact set is empty
negative_passages.docid: 76764
negative_passages.text: Find two closed subsets or real numbers such that $d(A,B)=0$ but $A\cap B=\varnothing$
negative_passages.docid: 33064
negative_passages.text: Powerset of set with empty sets
negative_passages.docid: 10472
negative_passages.text: Is every set a subset?
negative_passages.docid: 109219
negative_passages.text: How do the sets $\emptyset\times B,\ A\ \times \emptyset, \ \emptyset \times \emptyset $ look like?
negative_passages.docid: 88205
negative_passages.text: How can I define a topology on the empty set?
negative_passages.docid: 34099
negative_passages.text: Proving that the empty set is unique
negative_passages.docid: 9850
negative_passages.text: How many ways are there to choose 3 subsets $A,B,C$ of a set $\{1,2,3...n\}$ such that $ A \cap B \cap C = \emptyset $
negative_passages.docid: 84609
negative_passages.text: Unary intersection of the empty set
negative_passages.docid: 36631
negative_passages.text: Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?
negative_passages.docid: 97951
negative_passages.text: Is the void set (∅) a proper subset of every set?
negative_passages.docid: 130418
negative_passages.text: Is ${\{\emptyset,\{\emptyset\},\{\{\emptyset\}\},\{\{\{\emptyset\}\}\},...\}} $ a set?
negative_passages.docid: 150825
negative_passages.text: Is an empty set equal to another empty set?
negative_passages.docid: 67702
negative_passages.text: Minimal dense subset