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Let ACR. • We say that is an interior point of A if for some e > 0, Ve (x)C R. The set of all interior points of A will be denoted by A°. • We say that x is a boundary point of A if for every e > 0, Ve (x) N A#Ø and Ve (x)N A° Ø. The set of all boundary points of A will be denoted by aA. Show that • Ā = A° U aA.

Let ACR. • We say that is an interior point of A if for some e > 0, Ve (x)C R. The set of all interior points of A will be denoted by A°. • We say that x is a boundary point of A if for every e > 0, Ve (x) N A#Ø and Ve (x)N A° Ø. The set of all boundary points of A will be denoted by aA. Show that • Ā = A° U aA.

Advanced Engineering Mathematics
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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How do you prove the first bullet point?

Let ACR. • We say that is an interior point of A if for some e > 0, Ve (x)C R. The set of all interior points of A will be denoted by A°. • We say that x is a boundary point of A if for every e > 0, Ve (x) N A#Ø and Ve (x)N A° Ø. The set of all boundary points of A will be denoted by aA. Show that A = A° U ÐA. ĐA is a closed set.
Transcribed Image Text:Let ACR. • We say that is an interior point of A if for some e > 0, Ve (x)C R. The set of all interior points of A will be denoted by A°. • We say that x is a boundary point of A if for every e > 0, Ve (x) N A#Ø and Ve (x)N A° Ø. The set of all boundary points of A will be denoted by aA. Show that A = A° U ÐA. ĐA is a closed set.
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