A set F is called an Fo-set (or an Fo) if it is a countable union of closed sets. Likewise, a set G is called a Gs-set (or a Gs) if it is a countable intersection of open sets. Then show that (a) [0, 1] is a Gs set. (b) (a, b] is a both Gs and an Fo set. (c) Q is an Fo set, but not a Gs set.
A set F is called an Fo-set (or an Fo) if it is a countable union of closed sets. Likewise, a set G is called a Gs-set (or a Gs) if it is a countable intersection of open sets. Then show that (a) [0, 1] is a Gs set. (b) (a, b] is a both Gs and an Fo set. (c) Q is an Fo set, but not a Gs set.
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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