Homework Help is Here – Start Your Trial Now!
Math
Calculus
1.84 We call pa cluster point of E, provided that for all e > 0 there exists e e E such that 0 < le – pl < e. (See Defintion 2.1.1.) Let ECR be any set with the property that there is a cluster point p of E such that p ¢ E. Show that there exists an open cover of E that has no finite subcover. Justify your claims. (Note: Exercise 1.83 is an example of the claim of this exercise.) Definition 2.1.1 A point a is called a cluster point of the set D if and onły if for all 8 > 0 there exists x E D such that 0 < |x – a| < 8. Thus a cluster point a of a set D has the property that it is always possible to find points x E D for which x # a and yet x is as close to a as we like.

1.84 We call pa cluster point of E, provided that for all e > 0 there exists e e E such that 0 < le – pl < e. (See Defintion 2.1.1.) Let ECR be any set with the property that there is a cluster point p of E such that p ¢ E. Show that there exists an open cover of E that has no finite subcover. Justify your claims. (Note: Exercise 1.83 is an example of the claim of this exercise.) Definition 2.1.1 A point a is called a cluster point of the set D if and onły if for all 8 > 0 there exists x E D such that 0 < |x – a| < 8. Thus a cluster point a of a set D has the property that it is always possible to find points x E D for which x # a and yet x is as close to a as we like.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.3: Subgroups
Problem 27E: (See Exercise 26) Let A be an infinite set, and let H be the set of all fS(A) such that f(x)=x for...
See similar textbooks
icon
Related questions
Question
100%
1.84 O We call pa cluster point of E, provided that for all e > 0 there exists e e E such that 0 < le – pl < e. (See Defintion 2.1.1.) Let E CR be any set with the property that there is a cluster point p of E such that p ¢ E. Show that there exists an open cover of E that has no finite subcover. Justify your claims. (Note: Exercise 1.83 is an example of the claim of this exercise.) Definition 2.1.1 A point a is called a cluster point of the set D if and only if for all 8 >0 there exists x E D such that 0 < |x – a < 8. Thus a cluster point a of a set D has the property that it is always possible to find points x E D for which r a and yet x is as close to a as we like.
Transcribed Image Text:1.84 O We call pa cluster point of E, provided that for all e > 0 there exists e e E such that 0 < le – pl < e. (See Defintion 2.1.1.) Let E CR be any set with the property that there is a cluster point p of E such that p ¢ E. Show that there exists an open cover of E that has no finite subcover. Justify your claims. (Note: Exercise 1.83 is an example of the claim of this exercise.) Definition 2.1.1 A point a is called a cluster point of the set D if and only if for all 8 >0 there exists x E D such that 0 < |x – a < 8. Thus a cluster point a of a set D has the property that it is always possible to find points x E D for which r a and yet x is as close to a as we like.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS