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
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.1: Sets And Geometry
Problem 7E: Let A, B, and C lie on a straight line as shown near Exercise 8. Classify these claims as true or...
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