Answered: Example 5: B(0, t) = {(X1, X2); |X1| <… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.1: Rectangular Coordinate Systems

Problem 7E

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Example 5: B(0, t) = {(x1, x2); |X1| < t, |x₂| < t} in (R², ||· ||∞) is an open ball. But
{(x1x2,0) |x₁|< t, |x₂| < t} is not open in (R³, ||· ||∞). So the projection map
P: R³ R³.
.P(X1, X2, X3) = (x1, x2, 0) is not an open map. Whereas Q : R³ → R².
Q(X1, X2, X3) = (x1, x2) is an open map.

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