totally bounded वाक्य
उदाहरण वाक्य
मोबाइल
- A metric space is compact iff it is complete and totally bounded.
- A metric space is compact if and only if it is complete and totally bounded.
- The image of a totally bounded subset under a uniformly continuous function is totally bounded.
- The image of a totally bounded subset under a uniformly continuous function is totally bounded.
- Therefore both names ( cauchy-precompact and totally bounded ) can be used interchangeably.
- The Pacific Ocean is the only ocean which is almost totally bounded by subduction zones.
- Further, a uniformity is compact if and only if it is complete and totally bounded.
- A uniform space is compact if and only if it is both totally bounded and Cauchy complete.
- In fact, a metric space is compact if and only if it is complete and totally bounded.
- It turns out that the space is cauchy-precompact if and only if it is totally bounded.
- Combining these theorems, a uniform space is totally bounded if and only if its completion is compact.
- A set is totally bounded if, given any positive radius, it is covered by finitely many balls of that radius.
- A compact set in fact can be covered by finitely many balls of arbitrary small radius, because it is totally bounded.
- *PM : totally bounded uniform space, id = 8958 new !-- WP guess : totally bounded uniform space-- Status:
- *PM : totally bounded uniform space, id = 8958 new !-- WP guess : totally bounded uniform space-- Status:
- :* X is quasibarreled \ Longleftrightarrow in X ^ \ star if a set T is absorbed by each barrel, then T is totally bounded;
- The definition can be extended still further, to any category of spaces with a notion of compactness and Cauchy completion : a space is totally bounded if and only if its completion is compact.
- Alternatively, " X " is " right "-totally bounded if and only if it satisfies the definition for topological abelian groups above, using " right " translates.
- X ^ \ star is defined as the space of continuous linear functionls X'endowed with the topology of uniform convergence on totally bounded sets in X ( and the " stereotype second dual space"
- A topological group " X " is " left "-totally bounded if and only if it satisfies the definition for topological abelian groups above, using " left " translates.
- अधिक वाक्य: 1 2
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