Let (X, d) be a metric space. Suppose that (r,) is a sequence of points in X which converges to a point x € X, and (yn) is a sequence of points in X which converges to a point y € X. Prove that the sequence of real numbers, d(xn, Yn) converges to d(x, y).
Let (X, d) be a metric space. Suppose that (r,) is a sequence of points in X which converges to a point x € X, and (yn) is a sequence of points in X which converges to a point y € X. Prove that the sequence of real numbers, d(xn, Yn) converges to d(x, y).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Could you please construct a proof that uses topology? Thank you
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