   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.

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