Exercise 1. Consider R2 with its usual topology. Find the closure in R2 of each one of the following sets (no need to justify): a) Q x (R\ Q). b) {1/n / ne N, n ≥ 1} x (R\ {p/2" | p, n = N}). c) {(x, y) = R² | ||(x, y) ||2 E Q}, where ||(x, y)2 = √x² + y². Consider the subset SC R2 defined by S = {(x, y) = R² | x>0, and y ≤ x²}. d) Find the interior Int (S) of S in R2 (no need to justify). e) Find he closure S of S in R2 (no need to justify).

Exercise 1. Consider R2 with its usual topology. Find the closure in R2 of each one of the following sets (no need to justify): a) Q x (R\ Q). b) {1/n / ne N, n ≥ 1} x (R\ {p/2" | p, n = N}). c) {(x, y) = R² | ||(x, y) ||2 E Q}, where ||(x, y)2 = √x² + y². Consider the subset SC R2 defined by S = {(x, y) = R² | x>0, and y ≤ x²}. d) Find the interior Int (S) of S in R2 (no need to justify). e) Find he closure S of S in R2 (no need to justify).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 67E

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