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Let X be the plane. For x = (₁.2) and y = (v₁.32) in X, let a(z. y) = |-. (a) Show that is a pseudometric. (b) Describe the d-cell of radius r centered at the point (a, b). (e) Find the d-closure of S = {re X: +z<1}.

Let X be the plane. For x = (₁.2) and y = (v₁.32) in X, let a(z. y) = |-. (a) Show that is a pseudometric. (b) Describe the d-cell of radius r centered at the point (a, b). (e) Find the d-closure of S = {re X: +z<1}.

Advanced Engineering Mathematics
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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Basic Pseudometric Spaces
4. Let X be the plane. For x = (₁, 2) and y = (v₁.32) in X, let o(x, y) = 1-yil. (a) Show that is a pseudometric. (b) Describe the o-cell of radius r centered at the point (a, b). (e) Find the o-closure of S = {re X: + x < 1}.
Transcribed Image Text:4. Let X be the plane. For x = (₁, 2) and y = (v₁.32) in X, let o(x, y) = 1-yil. (a) Show that is a pseudometric. (b) Describe the o-cell of radius r centered at the point (a, b). (e) Find the o-closure of S = {re X: + x < 1}.
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