1. The standard analysis way to word this is:
A sequence {p_n} converges to p in X if and only if for every open neighborhood U of p, there exists an N such that for all n >= N, p_n is in U.
In other words, no matter what neighborhood of p you give me, the "tail end" of the sequence is completely contained in that neighborhood.
2. Adjoined means to put them together. So my new cover is
He's just extending the cover to include the entire space you're working in.
]]>PS. hit up sequence at wikipedia.
]]>What does it mean by "For all but finitely many"? is there an equivalent way to word it?
What does it mean by adjoined? Rudin didn't explain this term in his book
Thanks in advance : )
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