What does a term “space” mean in math? (Vector space, Metric space, Sample space and etc.)

Question

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In: Mathematics

Answer 1

a “space” is usually a “set” with a certain structure. A vector space is a set (of vectors), for which certain linear relations hold. A metric space is a set were some kind of distance is defined….

Of course the imprinted structure is kind of arbitrary, but certain simple structures (like the above) give rise to very rich relations (and applications).