Q1:- Let A, B, C, D, E be subsets of the Euclidean space R². Find their boundary, their interior, and their exterior. Conclude from here whether these sets are open, closed, or neither. a) A = (x E R² | d₂ (x,xo) ≤ 2}, where x₁ € R². b) B = Rx [a, b), where a, b E R, a < b. c) C = (a, b)² = (a, b) x (a, b), where a, b E R,a < b.
Q1:- Let A, B, C, D, E be subsets of the Euclidean space R². Find their boundary, their interior, and their exterior. Conclude from here whether these sets are open, closed, or neither. a) A = (x E R² | d₂ (x,xo) ≤ 2}, where x₁ € R². b) B = Rx [a, b), where a, b E R, a < b. c) C = (a, b)² = (a, b) x (a, b), where a, b E R,a < b.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Q1:- Let A, B, C, D, E be subsets of the Euclidean space R². Find their boundary, their
interior, and their exterior. Conclude from here whether these sets are open, closed, or
neither.
a) A = {x € R² | d₂ (x,xo) ≤ 2}, where x₁ € R².
b) B = Rx [a, b), where a, b E R, a < b.
c) C = (a, b)² = (a, b) x (a, b), where a, b € R, a < b.
d) D= (a) x [b, c), where a, b, c € R,b< c.
e) E = {a} x {b, c), where a, b, c E
R, b = c.
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