metric space in a sentence

Examples

1. :So you learn general topology first and then specialize into metric spaces.
2. Equivalently, in the case of a metric space, this can be expressed as
3. In fact, the Heine Borel theorem for arbitrary metric spaces reads:
4. The proof of the generalized theorem to metric space is similar.
5. For a function between metric spaces, uniform continuity implies Cauchy continuity.
6. Every compact metric space is complete, though complete spaces need not be compact.
7. Every metric space has a unique ( up to isometry ) dense subset.
8. Menger curvature may also be defined on a general metric space.
9. Includes such notions as convergence, separation axioms, metric spaces, dimension theory.
10. The unit interval is a complete metric space, locally path connected.