Exercise 2Part 3 and 4 only! 2{0} defined byp). In the plane R2, for v € R² \ {0}, define the open half line D, throughD₂ = {tv | t >0} CR².0 € DvDvSuppose 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.

Given in the plane ℝ2 , for v∈ℝ2-0, the open half line is defined by Dv=tv|t>0⊂ℝ2 c) To show that…

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...

See similar textbooks

Similar questions

Let all of the lines named be coplanar. Make a drawing to reach a conclusion. a If rs and st, then _. b If ab and bc, then _.
Let A, B, and C lie on a straight line as shown near Exercise 8. Classify these claims as true or false. a B lies between A and C. b AB is a ray with endpoint B.
Review Exercises In Review Exercises 22 to 24, M and N are the midpoints of FJ- and FH- respectively. Given: MN=x2+6 JH=2xx+2 Prove: x,MN,JH
In MNP for Exercise 29, medians MB, NA and PC intersect at centroid Q. a Find QB If MQ=8.2. b Find PQ if QC=72. c. Find AN if AQ=4.6 Exercises 27, 28
Which point P on XY partitions the directed segment from X to Y in the ratio 4 to 1?
Sketch the following sets of points in the x-y plane. {(x, x^2): x is in R}
Let ℓ be a line and let H be one of the half-planes bounded by ℓ. Prove that H ∪ ℓ is a convex set.
Prove that a finite projective plane of order n has n2 + n + 1 points andn2 + n + 1 lines.
7. What additional piece is needed to prove JMLK is a rhombus ?
Consider the infinite geometry R^2, where points are (x, y) ∈R and lines are ax + by + c = 0with a, b, c ∈R but not both a and b zero at the same time. Show that R^2, as defined above,is an Affine plane.
Prove or disprove that AS is congruent to SB (or that CS divides AB equally) if a line is drawn from vertex C to a point S in AB such that CS is perpendicular to AB.
Indicate on an xy-plane those points (x, y) for which the statement holds. |x − 3| ≤ 5 and |y + 2| < 5