Definition, Betydelse & Synonymer | Engelska ordet COMPACTNESS

Definition av COMPACTNESS

1. kompakthet

Exempel på hur du använder COMPACTNESS i en mening

• In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space.
• Nuvistors were made to compete with the then-new bipolar junction transistors, and were much smaller than conventional tubes of the day, almost approaching the compactness of early discrete transistor casings.
• In particular, a topology allows defining properties such as continuity, connectedness, and compactness, which were originally defined by means of a distance.
• There are many situations where another condition of topological spaces (such as normality, pseudonormality, paracompactness, or local compactness) will imply regularity if some weaker separation axiom, such as preregularity, is satisfied.
• More popular in the 19th and early 20th centuries was the Bolzano-Weierstrass criterion that every bounded infinite sequence admits a convergent subsequence, now called sequential compactness.
• Two lower-case letters in the range "a"-"s" were used instead, for reasons of simplicity and compactness.
• The compactness theorem for the propositional calculus is a consequence of Tychonoff's theorem (which says that the product of compact spaces is compact) applied to compact Stone spaces, hence the theorem's name.
• For compactness, the vulcanized rubber image with an adhesive foam backing may be attached to a cling vinyl sheet which allows it to be used with an acrylic handle for support.
• The message format was designed for compactness rather than flexibility, consistent with the slow dialup modems used in 1980.
• When in 1935 von Ohain designed his overall engine layout, he based it for compactness on a centrifugal impeller (centrifugal or radial compressor) and a radial inflow turbine.
• The name "weakly compact" refers to the fact that if a cardinal is weakly compact then a certain related infinitary language satisfies a version of the compactness theorem; see below.
• Some striking applications of ultraproducts include very elegant proofs of the compactness theorem and the completeness theorem, Keisler's ultrapower theorem, which gives an algebraic characterization of the semantic notion of elementary equivalence, and the Robinson–Zakon presentation of the use of superstructures and their monomorphisms to construct nonstandard models of analysis, leading to the growth of the area of nonstandard analysis, which was pioneered (as an application of the compactness theorem) by Abraham Robinson.
• The Lindelöf property is a weakening of the more commonly used notion of compactness, which requires the existence of a finite subcover.
• Some requirements for this problem are: contiguity, compactness, balance or equity, respect of natural boundaries, and socio-economic homogeneity.
• He introduced the new concept of compactness (Alexandrov himself called it "Bicompactness", and applied the term compact to only countably compact spaces, as was customary before him).
• Notions of compactness and completeness that are equivalent in finitary logic sometimes are not so in infinitary logics.
• Mahler's compactness theorem was generalized to semisimple Lie groups by David Mumford; see Mumford's compactness theorem.
• Considering the power set of T as a complete lattice with the subset inclusion order, where the supremum of a collection of sets is given by their union, the topological condition for compactness mimics the condition for compactness in join-semilattices, but for the additional requirement of openness.
• What fascinated him was the beautiful new style, the rhythmically arranged packing of sentences, the rigidity and purity of the language with a dramatic compactness, and the French strangeness which made the translation truly incomprehensible for amateur readers.
• These lyrics display a delicacy of form, a voluptuous horror, an imagistic compactness and suggestiveness, and, occasionally, a grotesque comic power that are absolutely unique.

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