   Chapter 16.3, Problem 31E

Chapter
Section
Textbook Problem

Determine whether or not the given set is (a) open, (b) connected, and (c) simply-connected.31. {(x, y) | 0 < y < 3}

(a)

To determine

Whether the given set is open or not.

Explanation

Given data:

Set is {(x,y)|0<y<3} .

The set {(x,y)|0<y<3} consists points on area between the horizontal lines y=0 and y=3 but not on the lines.

Draw the set {(x,y)|0<y<3} 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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