Space

:This article is about space — the scientific and philosophical concepts. For other uses of space, see space (disambiguation).

Mathematics and space

In mathematics, a 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.

Related Topics:
Mathematics - Set - Structure

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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.

Related Topics:
Vector space - Euclidean space - Banach space - Hilbert space - Metric space - Measure space

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As far as the concept of dimension is defined, this need not be 3: it can also be 0 (a point), 1 (a line), 2 (a plane), more than 3, 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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Kinds of mathematical spaces include:

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• Banach space
• Euclidean space
• Hilbert space
• Metric space
• Probability space
• Projective space
• Topological space
• Vector space