A Set with a global distance Function (the Metric ) which, for every two points in , gives the Distance between them as a Nonnegative Real Number . A metric space must also satisfy

- 1. Iff ,
- 2. ,
- 3. The Triangle Inequality .

**References**

Munkres, J. R. *Topology: A First Course.* Englewood Cliffs, NJ: Prentice-Hall, 1975.

Rudin, W. *Principles of Mathematical Analysis.* New York: McGraw-Hill, 1976.

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1999-05-26