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Problem 2.23. Let E CN be the set of even natural numbers. Give N the cofinite topology. What is E'? What is E?

Problem 2.23. Let E CN be the set of even natural numbers. Give N the cofinite topology. What is E'? What is E?

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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Solve 2.23 

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Definition 2.21. Let X be a space. Let A be a subset of X. We say that a point x E X is a limit point of A iff for every open set U in X containing x, (U \ {x})n A ± Ø. The set of limit points of A is denoted A'. Exercise 2.22. Let E C N be the set of even natural numbers. Give N the Ta topology (see Exercise 2.12). What is E'? What is E? Problem 2.23. Let E C N be the set of even natural numbers. Give N the cofinite topology. What is E'? What is E?
Transcribed Image Text:Definition 2.21. Let X be a space. Let A be a subset of X. We say that a point x E X is a limit point of A iff for every open set U in X containing x, (U \ {x})n A ± Ø. The set of limit points of A is denoted A'. Exercise 2.22. Let E C N be the set of even natural numbers. Give N the Ta topology (see Exercise 2.12). What is E'? What is E? Problem 2.23. Let E C N be the set of even natural numbers. Give N the cofinite topology. What is E'? What is E?
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