::Space (mathematics)


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A hierarchy of mathematical spaces: The inner product induces a norm. The norm induces a metric. The metric induces a topology.

In mathematics, a space is a set (sometimes called a universe) with some added structure.

Mathematical spaces often form a hierarchy, i.e., one space may inherit all the characteristics of a parent space. For instance, all inner product spaces are also normed vector spaces, because the inner product induces a norm on the inner product space such that:

<math> \left\| x \right\| = \sqrt{\langle x, x\rangle} .</math>

Modern mathematics treats "space" quite differently compared to classical mathematics.{{ safesubst:#invoke:Unsubst||date=__DATE__ |$B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }}

Space (mathematics) sections
Intro  History   Taxonomy of spaces   See also  Notes  Footnotes  References  External links  

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