Dense subset of dense subspace is dense
Statement
Suppose is a topological space and is a dense subset of . Suppose is a subset of that is a dense subset of under the subspace topology on from . Then, is also a dense subset of .
Suppose is a topological space and
is a dense subset of
. Suppose
is a subset of
that is a dense subset of
under the subspace topology on
from
. Then,
is also a dense subset of
.