Assertion: set | /r/HasProperty | dense
Facets:
value: nowhere
type: LOCATION
value: in its own subspace topology
type: LOCATION
value: always
type: DEGREE
value: y. notably
type: DEGREE
value: in itself
type: OTHER
Source sentences:
text: A set with no isolated point is said to be dense-in-itself (every neighbourhood of a point contains other points of the set).
text: Y. Notably, a set is always dense in its own subspace topology.
text: Indeed, a set is nowhere dense if and only if its closure is nowhere dense.
text: Indeed, a set is nowhere dense if and only if its closure is nowhere dense.
text: This set is nowhere dense, as it is closed and has an empty interior: any interval (a, b) is not contained in the set since the dyadic fractions in (a, b) have been removed.