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Show that a set A in ℝ2 is open in the Euclidean metric ⇔ it is open in the max metric.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 68E

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Question

Show that a set A in ℝ² is open in the Euclidean metric ⇔ it is open in the max metric.
Hint: As usual, there are two directions to prove in an ⇔. The picture on p73 of the notes may be somewhat helpful.

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