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Dummit and Foote, Abstract Algebra
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Silverman and Tate, Rational Points on Elliptic Curves
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Conway, Functions of One Complex Variable I
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Munkres, Topology
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Royden, Real Analysis
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1443 out of 100,000 projected words written.
Top 100 novels of all time
Reading Ulysses
IMDB top 250 films
Tengoku to jigoku next in queue.
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Vito Prosciutto: Teaching community college math on the road to a PhD.
Friday, June 03, 2005
00:32Definition of a topology: A question
A topology on a set X is a collection T of subsets of X having the following properties:It's that third item. Why must it be a finite subcollection? Can anyone give me a straightforward counterexample where the intersection of elements of an infinite subcollection doesn't work?
 The empty set and X are in T.
 The union of the elements of any subcollection of T is in T.
 The intersection of the elements of any finite subcollection of T is in T.
I suppose my other problem, is that Munkres hasn't really explained what a topology is for yet. I kind of feel like I'm looking at the abstract definition of a geometry without ever having seen any geometry before.