topological space vs mathematical space

topological space and mathematical space both are nouns.

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

As nouns, topological space and mathematical space are synonyms defined as:

topological space and mathematical space: (mathematics) any set of points that satisfy a set of postulates of some kind

topological space (noun)	mathematical space (noun)
(mathematics) any set of points that satisfy a set of postulates of some kind	(mathematics) any set of points that satisfy a set of postulates of some kind