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Nevermind, I was mistaken. "Countably compact" means every countable cover has a finite subcover. "Lindelof" means every cover has a countable subcover. "Compact" means every cover has a finite subcover. It is obvious that a countably compact space is compact if and only if
Lindelof.
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I added Jech's book as a reference. This is perhaps overkill, any book on Set Theory will define omega_1. (Kunen, Komjath, Just+Weese, Drake+Singh, Deiser, ...) Also some books in
Algebra and/or Analysis will define omega_1 and at least mention some basic properties.
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is not ω. Any continuous function from to the reals must be constant on for some α<ω
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I also added "Counterexamples in topology" for the topological properties.
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and in my topology reference. I'll go ahead and change it.
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