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#1 2009-03-29 08:44:27
- JaneFairfax
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- Registered: 2007-02-23
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Topologies on {a,b,c}
One of the exercise questions at the end of the third chapter of Sutherlands Introduction to Metric and Topological Spaces asks the reader to list all possible topologies on
(i) is easy:
.(iii) looks easy. The hint at the back of the book, though, says there are 29 of them! 
Okay, lets list them all.
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#2 2009-03-29 09:45:35
- JaneFairfax
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- Registered: 2007-02-23
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Re: Topologies on {a,b,c}
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#3 2009-03-29 10:00:08
- mathsyperson
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- Registered: 2005-06-22
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Re: Topologies on {a,b,c}
The remaining six are all isomorphic to each other.
Why did the vector cross the road?
It wanted to be normal.
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#4 2009-03-29 10:12:36
- JaneFairfax
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- Registered: 2007-02-23
- Posts: 6,868
Re: Topologies on {a,b,c}
Haha, I was wondering which were the ones I missed! 
Now I wonder what the list of all possible topologies for {a,b,c,d} is like. 
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