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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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 F set, but not a Gs set.
Transcribed Image Text: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 F set, but not a Gs set.
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