Noun:

মেট্রিক স্থান,

metric space's Usage Examples:

In mathematics, a metric space is a set together with a metric on the set.

In mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M.

first-countable, separable Hausdorff space (in particular, a separable metric space) has at most the continuum cardinality c {\displaystyle {\mathfrak {c}}}.

A set with a metric is called a metric space.

It can be thought of as a vector space (or affine space), a metric space, a topological space, a measure space, or a linear continuum.

discrete metric space to another bounded metric space is Lipschitz continuous, and any function from a discrete metric space to another metric space bounded.

manifold; consider the associated metric space ( M , d g ) .

} Relative to this metric space structure, one says that a path c.

metrizable topological space; that is, a space homeomorphic to a complete metric space that has a countable dense subset.

Most commonly M is a metric space and dissimilarity is expressed as a distance metric, which is symmetric.

of n {\displaystyle n} -dimensional normed spaces becomes a compact metric space, called the Banach–Mazur compactum.

transformation between metric spaces, usually assumed to be bijective.

Given a metric space (loosely, a set and a scheme for assigning distances between elements.

of a metric space (M, d) is bounded if there exists r > 0 such that for all s and t in S, we have d(s, t) < r.

(M, d) is a bounded metric space (or d.

generalization of a metric space in which the distance between two distinct points can be zero.

In the same way as every normed space is a metric space, every seminormed.

The utility of Cauchy sequences lies in the fact that in a complete metric space (one where all such sequences are known to converge to a limit), the.

uniformities is provided by the example of metric spaces: if (X, d) is a metric space, the sets U a = { ( x , y ) ∈ X × X : d ( x , y ) ≤ a } where a > 0 {\displaystyle.

In a complete metric space, a closed set is a set which is closed under the limit operation.

isometry group of a metric space is the set of all bijective isometries (i.

bijective, distance-preserving maps) from the metric space onto itself, with.

In a metric space M = ( X , d ) {\displaystyle M=(X,d)} , a set V {\displaystyle V} is.

In a metric space—that is, when a distance is defined—open sets are the sets that, with.

Synonyms:

Euclidean space; topological space; Hilbert space; mathematical space;

Antonyms:

dirty; fullness; validate; existence; valid;