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From Nordan Symposia
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==In mathematics==
==In mathematics==
Space is a [[set]], with some particular properties and usually some additional [[mathematical structure|structure]], such as the operations of addition or multiplication, for instance. 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.
Space is a [[set]], with some particular properties and usually some additional [[structure]], such as the operations of addition or multiplication, for instance. 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]].
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]].
