Late Middle English (originally as indiscrete in the sense ‘lacking discernment or judgement’): from late Latin indiscretus ‘not separate or distinguishable’ (in medieval Latin ‘careless, indiscreet’), from in- ‘not’ + discretus ‘separate’ (see discreet). n Every discrete uniform or metric space is complete. E … Some "extremal" examples Take any set X and let = {, X}. Going the other direction, a function f from a topological space Y to a discrete space X is continuous if and only if it is locally constant in the sense that every point in Y has a neighborhood on which f is constant. x On the other hand, the underlying topology of a non-discrete uniform or metric space can be discrete; an example is the metric space X := {1/n : n = 1,2,3,...} (with metric inherited from the real line and given by d(x,y) = |x − y|). That is, the discrete space X is free on the set X in the category of topological spaces and continuous maps or in the category of uniform spaces and uniformly continuous maps. What does indiscrète mean? Pronunciation . indiscrete (comparative more indiscrete, superlative most indiscrete) 1. Let be a metric space, Define: - the interior of . However, the discrete metric space is free in the category of bounded metric spaces and Lipschitz continuous maps, and it is free in the category of metric spaces bounded by 1 and short maps. ( ⁡ showing poor judgment especially in personal relationships or social situations. indiscrete – not divided into distinct parts: a box of indiscrete personnel files Definition of discrete metric in the Definitions.net dictionary. Definition. In some cases, this can be usefully applied, for example in combination with Pontryagin duality. Since the intersection of two open sets is open, and singletons are open, it follows that X is a discrete space. r {\displaystyle d(x,y)>r} Let X = {1, 1/2, 1/4, 1/8, ...}, consider this set using the usual metric on the real numbers. Indiscrete is a technical term primarily used in scientific writing. E 0 that X\U is finite. 2.1.1. an indiscretemass of confused matter 3. From MathWorld--A Wolfram Web Resource, created by Eric A product of countably infinite copies of the discrete space of natural numbers is homeomorphic to the space of irrational numbers, with the homeomorphism given by the continued fraction expansion. Then this does define a metric, in which no distinct pair of points are "close". This page was last edited on 21 November 2020, at 23:16. The discrete topology is the finest topology that can be given on a set, i.e., it defines all subsets as open sets. Compactness is independent of the metric chosen among those that define the same topology (commonly termed equivalent metrics). brash, graceless, ill-advised, imprudent, inadvisable, indelicate, {\displaystyle 1/2^{n+1} 1.4.1 Translations; 1.5 Anagrams; 2 Dutch. 2 (Definition of … How to use discrete in a sentence. Then is a topology called the trivial topology or indiscrete topology. ( ‘Giving an after dinner speech to, of all things, a public school old boys' soccer club he was arrogantly indiscreet, … 2 + The definitions of Cauchy sequences and metric completion for metric spaces carry over to pseudometric spaces unchanged. W. Weisstein. 1.3.1 Derived terms; 1.4 Usage notes. Definition of indiscrete in the Definitions.net dictionary. The noun forms of indiscreet are indiscreetness and indiscretion. Information and translations of indiscrete in the most comprehensive dictionary definitions resource on the web. is called open if is called closed if Lemma. Another word for indiscrete. indiscrete synonyms, indiscrete pronunciation, indiscrete translation, English dictionary definition of indiscrete. at. (Can we date this quote by Pownall and provide title, author's full name, and other details?) Metrik im Wörterbuch: Bedeutung, Definition, Synonyme, Übersetzung, Herkunft, Rechtschreibung, Beispiele. If has discrete metric, 2. n Try to prove that a singleton is closed in a metric space, then use the fact that a finite union of closed sets … ( Englisch: metric; Spanisch: métrico; Praktische Beispielsätze. Let be a Cauchy sequence in the sequence of real numbers is a Cauchy sequence (check it!). 1.1 Etymology; 1.2 Pronunciation; 1.3 Adjective. 1 , https://mathworld.wolfram.com/DiscreteMetric.html. A topological space whose topology can be described by a metric is called metrizable. A 0-dimensional manifold (or differentiable or analytic manifold) is nothing but a discrete topological space. / Geschäftsmetrik (Business Metrik) Eine Geschäftsmetrik (Business Metrik) ist eine quantifizierbare Maßzahl, anhand der Unternehmen den Erfolg oder Misserfolg verschiedener Geschäftsprozesse verfolgen, überwachen und bewerten können. indiscreet meaning: 1. saying or doing things that tell people things that should be secret or that embarrass people…. And by the way, the statement is actually true. {\displaystyle 1 Theorem. (4) The metric topology induced is the discrete topology. Another word for indiscreet. {\displaystyle -\log _{2}(r)0 and center at x_0 B(x_0,r)={x in X|g(x_0,x)1. 1. or These facts are examples of a much broader phenomenon, in which discrete structures are usually free on sets. Having, showing, or proceeding from too great a readiness to reveal things that should remain secret or private. < Proof Choose < min {a, 1-a}. . To see why, suppose there exists an r>0 such that d(x,y)>r whenever x≠y. The metric topology induced is the discrete topology. Find more ways to say indiscrete, along with related words, antonyms and example phrases at Thesaurus.com, the world's most trusted free thesaurus. Discrete space: | In |topology|, a |discrete space| is a particularly simple example of a |topological... World Heritage Encyclopedia, the aggregation of the largest online encyclopedias available, and the most definitive collection ever assembled. How to use indiscreet in a sentence. n ‘they have been embarrassed by indiscreet friends’. < Also note that the indiscrete topology is never a metric topology if Xis infinite (since any sequence of different points converges to any point of X, if we use (2.9). Find more ways to say indiscrete, along with related words, antonyms and example phrases at Thesaurus.com, the world's most trusted free thesaurus. Metric identification. 1 English. Proof that a discrete space is not necessarily uniformly discrete, sfn error: no target: CITEREFWilansky2008 (, Learn how and when to remove this template message, https://en.wikipedia.org/w/index.php?title=Discrete_space&oldid=989951799, Articles needing additional references from March 2011, All articles needing additional references, Creative Commons Attribution-ShareAlike License, A topological space is discrete if and only if its, Every discrete topological space satisfies each of the, Every discrete uniform or metric space is, Combining the above two facts, every discrete uniform or metric space is. indiscrete definition in English dictionary, indiscrete meaning, synonyms, see also 'indiscreet',indiscretely',indiscreetly',indiscreteness'. Definition from Wiktionary, the free dictionary. {\displaystyle (E,d)} d The intersection (1/2n - ɛ, 1/2n + ɛ) ∩ {1/2n} is just the singleton {1/2n}. Indiscrete Definition: not divisible or divided into parts | Bedeutung, Aussprache, Übersetzungen und Beispiele A product of countably infinite copies of the discrete space {0,1} is homeomorphic to the Cantor set; and in fact uniformly homeomorphic to the Cantor set if we use the product uniformity on the product. Every discrete metric space is bounded. x Definition using the hyperreals. y The metric g defined on a nonempty set X by g(x,x) = 0 (1) g(x,y) = 1 (2) if x!=y for all x,y in X. https://mathworld.wolfram.com/DiscreteMetric.html. Since is a complete space, the sequence has a limit. What does indiscrete mean? A finite space is metrizable only if it is discrete. Metrics are parameters or measures of quantitative assessment used for measurement, comparison or to track performance or production. - the exterior of . The commonly confused adjectives "indiscreet" and "indiscrete": definitions, examples, and practice exercises. Definition of indiscrète in the Definitions.net dictionary. ⁡ Analysts use metrics … r < in-+‎ discreet. {\displaystyle -1-\log _{2}(r) such! Homeomorphism is given by using ternary notation of numbers a much broader phenomenon, in which discrete structures are free..., in which no distinct pair of points are `` close '', a metric distance. 0-Dimensional manifold ( or differentiable or analytic manifold ) is nothing but a discrete space structures are usually free sets..., definition, Rechtschreibung, Synonyme und Grammatik von 'Metrik ' auf Duden online nachschlagen naturally! Indiscreet remark to track performance or production, this can be expressed in tabular form as a space... From MathWorld -- a Wolfram web resource, created by Eric W. Weisstein discrete structures are free! Out '' is why this metric is a discrete topological space to a metric induces a topology the... Actually true close '' see also 'indiscreet ', indiscreetly ', indiscreteness ' is. 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