Definition:Underlying Set

Abstract Algebra
Let $$\left({S, \circ}\right)$$ be an algebraic structure.

Then the underlying set of $$\left({S, \circ}\right)$$ is the set $$S$$.

Metric Spaces
Let $$\left({X, d}\right)$$ be a metric space.

Then the underlying set of $$\left({X, d}\right)$$ is the set $$X$$.