metric space वाक्य
उदाहरण वाक्य
मोबाइल
- A metric space is Lindel�f if and only if it is second-countable.
- Every metric space is therefore, in a natural way, a topological space.
- A metric space is compact iff it is complete and totally bounded.
- Every isometry group of a metric space is a subgroup of isometries.
- For example, a metric space can be regarded as an enriched category.
- The definition can be generalized to functions that map between metric spaces.
- In general, a metric space may have no geodesics, except constant curves.
- The space has a metric ( see metric space for details ).
- Thus for metric spaces we have : compactness = cauchy-precompactness + completeness.
- In a general metric space, however, a Cauchy sequence need not converge.
- :So you learn general topology first and then specialize into metric spaces.
- Equivalently, in the case of a metric space, this can be expressed as
- In fact, the Heine Borel theorem for arbitrary metric spaces reads:
- The proof of the generalized theorem to metric space is similar.
- For a function between metric spaces, uniform continuity implies Cauchy continuity.
- Every compact metric space is complete, though complete spaces need not be compact.
- Every metric space has a unique ( up to isometry ) dense subset.
- Menger curvature may also be defined on a general metric space.
- Includes such notions as convergence, separation axioms, metric spaces, dimension theory.
- The unit interval is a complete metric space, locally path connected.
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