totally bounded meaning in Hindi

Examples

1. A metric space is compact iff it is complete and totally bounded.
2. A metric space is compact if and only if it is complete and totally bounded.
3. The image of a totally bounded subset under a uniformly continuous function is totally bounded.
4. The image of a totally bounded subset under a uniformly continuous function is totally bounded.
5. Therefore both names ( cauchy-precompact and totally bounded ) can be used interchangeably.
6. The Pacific Ocean is the only ocean which is almost totally bounded by subduction zones.
7. Further, a uniformity is compact if and only if it is complete and totally bounded.
8. A uniform space is compact if and only if it is both totally bounded and Cauchy complete.
9. In fact, a metric space is compact if and only if it is complete and totally bounded.
10. It turns out that the space is cauchy-precompact if and only if it is totally bounded.