Примери за използване на Metric space на Английски и техните преводи на Български
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Is called a metric space.
Other major contributions by Kuratowski were to compactness and metric spaces.
Directions in metric spaces.
The letter discusses Urysohn's metrization theorem andhis construction of a universal separable metric space.
Let where is a metric space.
Because Cauchy sequences require the notion of distance,they can only be defined in a metric space.
Dynamical Systems 1 Suppose that is a compact metric space and is a continuous function.
We saw that every metric space has a completion, that is can be embedded isometrically in a complete metric space.
Let(S, d) be a complete metric space.
The isometric imbedding of metric spaces into Hilbert space and positive definite functions.
Assume that is a seperable metric space.
A very similar argument proves that every metric space can be embedded in a minimal way into a complete metric space.
Continuous functions between metric spaces.
In it he introduced the concept of a metric space, although he did not invent the name'metric space' which is due to Hausdorff.
Geometry(Codes and designs in polynomial metric spaces).
The construction of a universal metric space, containing an isometric image of any metric space, was one of Urysohn's last results.
The first volume of this work was the major source on metric spaces for several decades.
It presents the theory of dimension for separable metric spaces with what seems to be an impossible mixture of depth, clarity, precision, succinctness, and comprehensiveness.
Another important aspect of Urysohn's ideas was the fact that he presented them in the context of compact metric spaces.
By Fréchet and others,had created a theory of topological and metric spaces in his famous book Grundzüge der Mengenlehre published in 1914.
A year later, in 1914, Hausdorff published his famous text Grundzüge der MengenlehreⓉ which builds on work by Fréchet andothers to created a theory of topological and metric spaces.
Banach begins with a chapter on Lebesgue integration followed by a chapter on metric spaces(but I couldn't find a mention of either Hilbert or Stone in his book).
Around the time Whyburn went to the University of Virginia he began working on homology theory andexamined different notions of convergence in the space of all subsets of a compact metric space.
He succeeded in creating a theory of topological and metric spaces into which the previous results fitted well, and he enriched it with many new notions and theorems.
Dowker's doctoral thesis extended basic results in homotopy theory from compact metric spaces to normal and parametric spaces. .
His first pure mathematical work was on metric spaces, an extension of Steinitz 's work to infinite dimensional vector spaces, and some beautiful results on differential geometry.
Hausdorff, building on work by Fréchet and others,had created a theory of topological and metric spaces in his famous book Grundzüge der Mengenlehre published in 1914.
In his dissertation of 1906, discussed above,he started a whole new area with his investigations of functionals on a metric space and formulated the abstract notion of compactness.
The aim here is to provide a more leisurely approach to the theory of the topology of metric spaces, a subject which is not only the basis of functional analysis but also unifies many branches of classical analysis.
From the modern point of view, the Grundzüge contained, in addition to other special topics,the beginnings of the theories of topological and metric spaces, which are now included in all textbooks on the subject.