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2 {0} defined by p). In the plane R², for v € R² \ {0}, define the open half line D, through D₂ = {tv | t >0} CR². 0 € Dv Dv Suppose v R²\{0} is given. a) Show that the subset R² \ D, is not an open subset of R². b) For w DU {0}, show that the set R² \ D is a neighborhood of w. c) Show that the set R² \ D, is not a neighborhood of 0. d) What is the closure of D.

2 {0} defined by p). In the plane R², for v € R² \ {0}, define the open half line D, through D₂ = {tv | t >0} CR². 0 € Dv Dv Suppose v R²\{0} is given. a) Show that the subset R² \ D, is not an open subset of R². b) For w DU {0}, show that the set R² \ D is a neighborhood of w. c) Show that the set R² \ D, is not a neighborhood of 0. d) What is the closure of D.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter1: Line And Angle Relationships
Section1.1: Early Definitions And Postulates
Problem 36E: Consider noncoplanar points A, B, C, and D. Using three points at a time such as A, B, and C, how...
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Exercise 2 Part 3 and 4 only!
2 {0} defined by p). In the plane R2, for v € R² \ {0}, define the open half line D, through D₂ = {tv | t >0} CR². 0 € Dv Dv Suppose v € R2 \ {0} is given. a) Show that the subset R2 \ D, is not an open subset of R². b) For w DU {0}, show that the set R² \ D, is a neighborhood of w. c) Show that the set R² \ D, is not a neighborhood of 0. d) What is the closure of Dv.
Transcribed Image Text:2 {0} defined by p). In the plane R2, for v € R² \ {0}, define the open half line D, through D₂ = {tv | t >0} CR². 0 € Dv Dv Suppose v € R2 \ {0} is given. a) Show that the subset R2 \ D, is not an open subset of R². b) For w DU {0}, show that the set R² \ D, is a neighborhood of w. c) Show that the set R² \ D, is not a neighborhood of 0. d) What is the closure of Dv.
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