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}

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