Recent content by Zetta

Thank you dx like before, you are giving me the most precise answer that I possibly can get, it seems even before I post my new question you knew what is in my mind!

So, can I say that e.g. "Pi1(S^1)=Z" means that: "The set of homotopy rel {0,1} classes of closed paths starting and ending at any point say x " in S^1 (which is a group) is homomorphic (actually isomorphic) to Z i.e. there is a homomorphism of groups between Pi1(S^1) and Z where "+ in Z"...

Sorry for these easy quastions, but if you see my lec notes(pdf) you might agree that there are some ambguities there for some one like me.

I mean for example in Pi1(S^2,1)={1}, this "{1}" exactly refers to what?

I have a question to clear up definitions for myself: When we calculate (or talk about) Pi1(X,x) do we actually calculate |Pi1(X,x)|? I mean "the number of equivalent classes like [a] w.r.t x in X"? For example if that is the case I can imagine what Pi1(S^2,(1,0)) means, but if that is not the...

Yes, I got that with your very nice and clear explanation. "Holes"! And what I learned from your answer is that when thinking about definitions don't let your brain to be lazy and bring the simplest possible space like R^2 (for example). Thank you very much

I meant this, please see the attachement.

Sorry, You did answer to the question number 1.

Thank you for the great help, brief and efficient! Just to check that I am on the right track now, 1.Can I say this is related to (because of) "discontinuaty of the choice of paths" between A and B? 2. Can I say in an "8" shape for example the top part and the bottom parts belong to two...

What I understand from the definition of the fundamental group is: Pi1(X.x) is "the set of rel {0,1} homotopy classes [a] of closed paths" Ok, when I think about one [a] it consists of all: 1.Closed paths like a and b with a(0)=a(1)=x & b(0)=b(1)=x --->since they are closed. 2.And since...