metric space sentence in Hindi

Examples

1. A metric space is Lindel�f if and only if it is second-countable.
2. Every metric space is therefore, in a natural way, a topological space.
3. A metric space is compact iff it is complete and totally bounded.
4. Every isometry group of a metric space is a subgroup of isometries.
5. For example, a metric space can be regarded as an enriched category.
6. The definition can be generalized to functions that map between metric spaces.
7. In general, a metric space may have no geodesics, except constant curves.
8. The space has a metric ( see metric space for details ).
9. Thus for metric spaces we have : compactness = cauchy-precompactness + completeness.
10. In a general metric space, however, a Cauchy sequence need not converge.