Metric Space

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

1. $g(x,y)=0$ Iff $x=y$,

2. $g(x,y)=g(y,x)$,

3. The Triangle Inequality $g(x,y)+g(y,z)\geq g(x,z)$.

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.