   Chapter 16.3, Problem 33E

Chapter
Section
Textbook Problem

Determine whether or not the given set is (a) open, (b) connected, and (c) simply-connected.33. {(x, y) | 1 ⩽ x2 +y2 ⩽ 4, y ⩾ 0}

(a)

To determine

Whether the given set is open or not.

Explanation

Given data:

Set is {(x,y)|1<x2+y2<4,y0} .

The set {(x,y)|1<x2+y2<4,y0} possesses a semi-annual region located in upper half-plane between the circles with origin as center and of radii 1 and 2 respectively.

Draw the set {(x,y)|1<x2+y2<4,y0} as shown in Figure 1

(b)

To determine

Whether the given set is connected or not.

(c)

To determine

Whether the given set is simply-connected or not.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

In Exercises 4756, solve the given equation for the indicated variable. 4=2x

Finite Mathematics and Applied Calculus (MindTap Course List)

For and

Study Guide for Stewart's Multivariable Calculus, 8th

0 2 −2 does not exist

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 