- #1
GatorPower
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Homework Statement
Is A = {0} union {1/n | n [tex]\in[/tex] {1,2,3,...}} compact in R?
Is B = (0,1] compact in R?
Homework Equations
Definition of compactness, and equivalent definitions for the space R.
The Attempt at a Solution
A is compact, but I can't seem to find a plausible proof of it... It should be homeomorphic to [0,1] and then compactness would follow if I can do that?
B is not compact. A open cover could be C = {(1/n,1] | n [tex]\in[/tex] {1,2,3,...}} which contains no finite subcollection that covers B (atleast my textbook says so, but I don't quite understand that).
How would you prove compactness (or not) on these sets?