21.) 0=f(x,yo/xto cmd у хоз and

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
21
•Show that the subsets of the plane are open.
18.) A = {(x,y) -1 < x < 1₁ -1 < y ≤1}
19.) B= {(x, y²ly >0}
| 20.1 C = {(x₁y) |2 < x² + y ² <4}
21.) 0= {(x, y) / x +0 andy +0}
Transcribed Image Text:•Show that the subsets of the plane are open. 18.) A = {(x,y) -1 < x < 1₁ -1 < y ≤1} 19.) B= {(x, y²ly >0} | 20.1 C = {(x₁y) |2 < x² + y ² <4} 21.) 0= {(x, y) / x +0 andy +0}
Expert Solution
Step 1

The given set is D=x,y:x0, y0

 

A set S is called open in the plane 2 all its points are interior points.

A point a,bS is called an interior point of S if there exists a δ>0 such that for all points x,y-a,b<δ

x,yS.

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