A set F is called an Fo-set (or an Fo) if it is a countable union ofclosed sets. Likewise, a set G is called a Gs-set (or a Gs) if it is acountable 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 F set, but not a Gs set.

a) Take An=( -1/n , 1+ 1/n ) , which is open Then taking intersection from n=1 to infinity we will…

Answered: A set F is called an Fo-set (or an Fo)…

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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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.