I would like to have an answer Establish whether the following proposition are trueor false. Justify the answer and in case a proposition is false, provide a suitablecounterexample.a) A convergent sequence in a metric space is a Cauchy sequence.b Let S be a set of R*. If there exists a convergent sequence {rn} such that{xn} → ro, ro E S, then S is closed.c) An upper hemicontinuos correspondence has the closed graph propertyd) Let X CR be a set and f: X X be a function. If X is compact and convex,then f admits a fixed point.e) Let V and U two vector spaces of finite dimension and let l: V →U be a linearfunction. If ker l = {0}, then I is onto.f) Consider a vector space V and let W be a subset of V.If 0 € W,then W is a vector subspace of V

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Answered: or false. Justify the answer and in…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.1: Infinite Sequences And Summation Notation

Problem 74E

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