- #31
mistermath
- 52
- 0
Here is my opinion on this. There are two paths you can take. One is, you can try and get an "ok" grasp on foundations of mathematics in order to prepare yourself for topology, or you can assume the foundations and go on.
If you are studying set theory, then why not study mathematical logic first (well formed formulas etc), then move up to set theory then move up to topology. This is imo a waste of time since most of the math you'll ever do assumes this stuff.
Or you can (this is the choice I recommend) just skip set theory and do topology.
All you need to know are the basics:
-What a set is.
-What a union and intersection is.
-De Morgan's Laws
-FACT: If I give you a set filled with an uncountable number of objects, you can pick an object from it. (called the axiom of choice).
I believe that if you pick up Munkrees (Like someone mentioned earlier) you can do the first 9 sections, skip 10/11 and learn all the topology you want, well worth the $50. Even feel free to skip the first 9 sections if you are decent with bijections, peano etc.
If you are studying set theory, then why not study mathematical logic first (well formed formulas etc), then move up to set theory then move up to topology. This is imo a waste of time since most of the math you'll ever do assumes this stuff.
Or you can (this is the choice I recommend) just skip set theory and do topology.
All you need to know are the basics:
-What a set is.
-What a union and intersection is.
-De Morgan's Laws
-FACT: If I give you a set filled with an uncountable number of objects, you can pick an object from it. (called the axiom of choice).
I believe that if you pick up Munkrees (Like someone mentioned earlier) you can do the first 9 sections, skip 10/11 and learn all the topology you want, well worth the $50. Even feel free to skip the first 9 sections if you are decent with bijections, peano etc.