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Show that the given collection F is an open cover for S such that it does not contain a finite subcover and so S is not compact. (a) S = (0, 2); and F = { U₂ | n ¤ N } where Un = (1, 2-1) (b) S = (0, ∞); and F = { Un | n € N} where Un = (0, n)

Show that the given collection F is an open cover for S such that it does not contain a finite subcover and so S is not compact. (a) S = (0, 2); and F = { U₂ | n ¤ N } where Un = (1, 2-1) (b) S = (0, ∞); and F = { Un | n € N} where Un = (0, n)

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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Help me answer number 9.
(9) Show that the given collection F is an open cover for S such that it does not contain a finite subcover and so S is not compact. (a) S = (0, 2); and F = { U₂ | n € N } where Un = (1, 2-1⁄2) (b) S = (0, ∞); and F = { Un | n ≤ N} where Un = (0, n)
Transcribed Image Text:(9) Show that the given collection F is an open cover for S such that it does not contain a finite subcover and so S is not compact. (a) S = (0, 2); and F = { U₂ | n € N } where Un = (1, 2-1⁄2) (b) S = (0, ∞); and F = { Un | n ≤ N} where Un = (0, n)
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