(3) Let R² and R be endowed with their Euclidean metrics. (a) Show that projections p₁(x, y) = x and p₂(x, y) = y are continuous. (b) Show that the direct image of an open set under p₁ or på is open.
(3) Let R² and R be endowed with their Euclidean metrics. (a) Show that projections p₁(x, y) = x and p₂(x, y) = y are continuous. (b) Show that the direct image of an open set under p₁ or på is open.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 8E
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![(3) Let R² and R be endowed with their Euclidean metrics.
(a) Show that projections p₁(x, y) = x and p₂(x, y) = y are continuous.
(b) Show that the direct image of an open set under p₁ or på is open.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c557725-037f-4839-bada-f183764fca9b%2F328c47ee-bf14-44ed-bfca-9c8e5665b7b7%2Fvls3d7i_processed.png&w=3840&q=75)
Transcribed Image Text:(3) Let R² and R be endowed with their Euclidean metrics.
(a) Show that projections p₁(x, y) = x and p₂(x, y) = y are continuous.
(b) Show that the direct image of an open set under p₁ or på is open.
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