Metric Space

A metric space is a set  with a global distance function (the metric ) that, 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, 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 2000.

Rudin, W. Principles of Mathematical Analysis, 3rd ed. New York: McGraw-Hill, 1976.