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Compact Sets and Compact Exhaustions

Definition: Let omega be a domain in C. Then e compact exhaustion {Ek} of omega is
1. Ek are all compact, Ek is contained in Ek+1 for all k
2. Union of Ek=omega
3. Any compact set K contained in omega is contained in some Ek

Problem. Find an example of Ek's satisfying 1 and 2 but not 3 for omega=unit disk

Solution Summary

Compact sets and compact exhaustions are investigated.