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What is required to learn topology?
I'm considering trying to learn at least the basics on my own, with not much of a mathematical background. I'll be taking Calculus I over the summer, and preparing for Calculus II through a supplementary book. Is it possible to try this junk with this little knowledge? I'd say I understand my current math easily. thanks!
2 Answers
- ?Lv 78 years agoFavorite Answer
Oh sure. Topology is really quite straight-forward. Mostly you'll need to grasp definitions. After that, a few theorems and you're home free. I'd start with Walter Rudin's book on real analysis (which is effectively point-set topology). A really good book on topology was authored by Robert Brown of UCLA in the mid-1980s.
The most important things to learn are:
1. Open sets
2. Closed sets
3. Compactness
4. Completeness
5. Differences between T1, T2, T3 and T4 spaces
6. Recognition that "metric" is not a topological property
7. Tychonoff's Theorem and Urysohn's Lemma
- 4 years ago
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