Assertion: set's subset | /r/HasProperty | dense
Facets:
value: nowhere
type: LOCATION
value: equivalently
type: DEGREE
value: in itself
type: MANNER
Source sentences:
text: Every non-empty subset of a set X equipped with the trivial topology is dense, and every topology for which every non-empty subset is dense must be trivial.
text: Finally, a subset \(D\) of \(P\) is called dense if for every \(p\in P\)
text: A subset without isolated points is said to be dense-in-itself.
text: Equivalently, a subset of a topological space is nowhere dense if and only if the interior of its closure is empty.
text: Every subset of a nowhere dense set is nowhere dense, and the union of finitely many nowhere dense sets is nowhere dense.