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79 topology space then Theorem: Let x be a 1- A set is closed iff every limit point of A is in A (ASA) 2- A set A is open iff no limit point of A is in A. (JPA) A) 3- The union of A and the set of all limit. points of A is closed set 4 AAUA -proof: (AVA' closed) Theorem: Let A be a subset in topology space x then 1- A YEA/y is not limit point of A°}. 2- (A) = A -3- (F (A)) = A°U (A²)°. 1 التاريخ الموضوع : 4-(A)=A-A°-A-(A°)°- 5-A-AUF (A)- 6- A° - A-F (A) 7 A is closed iPP F(A) ≤A- 8- A is open iff AAF (A) = 6.

79 topology space then Theorem: Let x be a 1- A set is closed iff every limit point of A is in A (ASA) 2- A set A is open iff no limit point of A is in A. (JPA) A) 3- The union of A and the set of all limit. points of A is closed set 4 AAUA -proof: (AVA' closed) Theorem: Let A be a subset in topology space x then 1- A YEA/y is not limit point of A°}. 2- (A) = A -3- (F (A)) = A°U (A²)°. 1 التاريخ الموضوع : 4-(A)=A-A°-A-(A°)°- 5-A-AUF (A)- 6- A° - A-F (A) 7 A is closed iPP F(A) ≤A- 8- A is open iff AAF (A) = 6.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.4: Definition Of Function
Problem 57E
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79 topology space then Theorem: Let x be a 1- A set is closed iff every limit point of A is in A (ASA) 2- A set A is open iff no limit point of A is in A. (JPA) A) 3- The union of A and the set of all limit. points of A is closed set 4 AAUA -proof: (AVA' closed) Theorem: Let A be a subset in topology space x then 1- A YEA/y is not limit point of A°}. 2- (A) = A -3- (F (A)) = A°U (A²)°. 1 التاريخ الموضوع : 4-(A)=A-A°-A-(A°)°- 5-A-AUF (A)- 6- A° - A-F (A) 7 A is closed iPP F(A) ≤A- 8- A is open iff AAF (A) = 6.
Transcribed Image Text:79 topology space then Theorem: Let x be a 1- A set is closed iff every limit point of A is in A (ASA) 2- A set A is open iff no limit point of A is in A. (JPA) A) 3- The union of A and the set of all limit. points of A is closed set 4 AAUA -proof: (AVA' closed) Theorem: Let A be a subset in topology space x then 1- A YEA/y is not limit point of A°}. 2- (A) = A -3- (F (A)) = A°U (A²)°. 1 التاريخ الموضوع : 4-(A)=A-A°-A-(A°)°- 5-A-AUF (A)- 6- A° - A-F (A) 7 A is closed iPP F(A) ≤A- 8- A is open iff AAF (A) = 6.
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