subspace vs mathematical space

subspace and mathematical space both are nouns.

Word	Noun	Adjective	Verb	Adverb
subspace	Yes	No	No	No
mathematical space	Yes	No	No	No

As nouns, mathematical space is a hypernym of subspace; that is, mathematical space is a word with a broader meaning than subspace:

subspace: a space that is contained within another space
mathematical space: (mathematics) any set of points that satisfy a set of postulates of some kind

Other hypernyms of subspace include topological space.

subspace (noun)	mathematical space (noun)
a space that is contained within another space	(mathematics) any set of points that satisfy a set of postulates of some kind