In Mathematics

Space is a set, with some particular properties and usually some additional structure. It is not a formally defined concept as such, but a generic name for a number of similar concepts, most of which generalize some abstract properties of the physical concept of space.

In particular, a vector space and specifically a Euclidean space can be seen as generalizations of the concept of a Euclidean coordinate system. Important varieties of vector spaces with more imposed structure include Banach space and Hilbert space. Distance measurement is abstracted as the concept of metric space and volume measurement leads to the concept of measure space.

As far as the concept of dimension is defined, although three-dimensional space is the most commonly thought of dimensional space, the number of dimensions for a space to exist need not be three: it can also be zero, one, two, more than three, finite or infinite, and with some definitions, a non-integer value. Mathematicians often study general structures that hold regardless of the number of dimensions

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