Requirements - Topology

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MATHNEM

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Hello everybody,

Is it necessary to have taken a course in Set theory in order to have a better understanding in a first Topology course? Or, Can I handle it with knowledge of vector calculus and linear algebra?

Thanks in advance.
 
MATHNEM said:
Is it necessary to have taken a course in Set theory in order to have a better understanding in a first Topology course? Or, Can I handle it with knowledge of vector calculus and linear algebra?
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The answer depends on what you mean by Set Theory.
I would have assumed that anyone taking vector calculus and linear algebra would have had a course in foundations that includes basic naive set theory and basic logic. So I say that a course in foundations of mathematics should be required before taking a topology course.

On the other hand, if you mean an advanced course set theory then the answer is no.
 
In engineering courses, often Linear algebra and Vector calculus are often taught without Foundation Theories.

Then again, I do not think topology is one of the subjects taught in engineering.
 
Yeah, I meant an advanced one. I'm majoring in pure math and I had a course called foundations of mathematics, which included basic set theory and some first-order logic stuff, but I thought it'd be necessary to have learned more about advanced theories such as the one of cardinal numbers, that's why I asked.

Thanks for your answers.
 
MATHNEM said:
Yeah, I meant an advanced one. I'm majoring in pure math and I had a course called foundations of mathematics, which included basic set theory and some first-order logic stuff, but I thought it'd be necessary to have learned more about advanced theories such as the one of cardinal numbers, that's why I asked.
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I assumed that you meant undergraduate course in topology. So you course in foundations should be fine. If I were you, I would find out what textbook is usually used and the have a look at it. Or go to the library is look at several different topology textbooks. You are the best person to judge the strength of your background it set theory.
 
Undergraduate.
Well, I'd already done it. I know they follow Elementary Topology (Gemignani) and look at some theorems in Topology (Munkres). Have you used any of them? Would you mind giving your opinion?
 
An undergraduate text in topology will almost certainly review the set theory required for the rest of the book. Usually in a first chapter or an appendix.The first chapter in Munkres will give you everything you need to know (including the exercises).
 
daon2 said:
An undergraduate text in topology will almost certainly review the set theory required for the rest of the book. Usually in a first chapter or an appendix.The first chapter in Munkres will give you everything you need to know (including the exercises).
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OK. I'll start with it.

Thank you all for the advise.
 
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