A vector space (over some field) with an additional binary operation, a vector-valued product between vectors, which is bilinear over vector addition and scalar multiplication. (N.B.: such bilinearity implies distributivity of the vector multiplication with respect to the vector addition, which means that such a vector space is also a ring.)
A mathematical object comprising representations of a space and of its spatial relationships.
A mathematical system that deals with spatial relationships and that is built on a particular set of axioms; a subbranch of geometry which deals with such a system or systems.
The observed or specified spatial attributes of an object, etc.
The branch of mathematics dealing with spatial relationships.