Let S1 = {(xy)/ x22y-1), S2 = {(x.y)/ x $3, 15 y 5} and S3 = {(x.y)/ O< x<3, 15ys5}. Then: O s1 and S2 are compact subspaces of R. Only S2 is a compact subspace of R. None of S1, S2 and S2 is compact in R. S2 and S3 are compact subspaces of R.

Let S1 = {(xy)/ x22y-1), S2 = {(x.y)/ x $3, 15 y 5} and S3 = {(x.y)/ O< x<3, 15ys5}. Then: O s1 and S2 are compact subspaces of R. Only S2 is a compact subspace of R. None of S1, S2 and S2 is compact in R. S2 and S3 are compact subspaces of R.

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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Let S1 = {(xy)/ x22y-1), S2 ((x.y)/ x $3, 1s y s5} and S3 = {(x.y)/ O< x<3, 1sys5}. Then:
O s1 and S2 are compact subspaces of R.
Only S2 is a compact subspace of R.
None of S1, S2 and S2 is compact in R.
S2 and S3 are compact subspaces of R.
A closed interval is not homeomorphic to neither an open interval nor a half open
interval.

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