Euclidean -space is the Space of all -tuples of Real Numbers, (, , ..., ) and is denoted . is a Vector Space and has Lebesgue Covering Dimension . Elements of are called -Vectors. is the set of Real Numbers (i.e., the Real Line), and is called the Euclidean Plane. In Euclidean space, Covariant and Contravariant quantities are equivalent so .

**References**

Gray, A. ``Euclidean Spaces.'' §1.1 in *Modern Differential Geometry of Curves and Surfaces.*
Boca Raton, FL: CRC Press, pp. 2-4, 1993.

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1999-05-25