Metric space

In mathematics, a metric space is a set where a notion of distance between elements of the set is defined. The metric space which most closely corresponds to our intuitive understanding of space is the 3-dimensional Euclidean space. The Euclidean metric of this space defines the distance between two points as the length of the straight line connecting them. The geometry of the space depends on the metric chosen, and by using a different metric we can construct interesting non-Euclidean geometries such as those used in the theory of general relativity.

Related Topics:
Mathematics - Set - Distance - Euclidean space - Euclidean metric - Straight line - Geometry - Non-Euclidean geometries - General relativity

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A metric space induces topological properties like open and closed sets which leads to the study of even more abstract topological spaces.

Related Topics:
Topological properties - Open - Closed set - Topological space

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