How To Use Metric space In A Sentence

If the space is a socalled metric space, it is usually expected that the underlying automorphism shall at least be isometric, meaning that the transformations preserve the distance between any pair of points.
SYMMETRY AND ASYMMETRY

Acoustics, the geometric space figure that is made up of the acoustic foci of an acoustic lens, mirror, or other acoustic optical system and is the acoustic counterpart of an extended source of sound.

Now, to a mathematician (and I am one of those), a metric is a nonnegative function of two points in a metric space (socalled because it is a set on which a metric is defined) that tells something about how far apart (often in quite nonintuitive ways) the two points are.
No Uncertain Terms

A Banach space is a real or complex normed vector space that is complete as a metric space under the metric induced by the norm.

If the space is a socalled metric space, it is usually expected that the underlying automorphism shall at least be isometric, meaning that the transformations preserve the distance between any pair of points.
SYMMETRY AND ASYMMETRY

Any metric space is an open subset of itself.