Find an example of a nonempty set satisfying: • Open, every point is a limit point • Closed, every point is a limit point • Closed, every point is a limit point, nowhere dense in R
Find an example of a nonempty set satisfying: • Open, every point is a limit point • Closed, every point is a limit point • Closed, every point is a limit point, nowhere dense in R
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 20E: Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not...
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Question
Find an example of a nonempty set satisfying:
• Open, every point is a limit point
• Closed, every point is a limit point
• Closed, every point is a limit point, nowhere dense in R
Expert Solution
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Step 1
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Just because a nonempty open set contains only limit points does not mean that the set contains all its limit points. For example, all points in the open interval (0,1) are limit points, but this set does not contain the limit points 0 and 1.
- The closed subset of R , provides that the every point within this interval is a limit point.
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