Recent content by Mikaelochi

Do you know a good source on that?

I understand that a homotopy is a continuous deformation. The only thing I really remember is something in my notes like this: F(s, 0) = a(s) for 0≤s≤1 and F(s, 1) = a * Id(s). Basically I have to construct some sort of piece-wise function such that I go something like two loops half of the time...

So, this problem I sort of get conceptually but I don't know how I can possibly rewrite (idX)∗ : π1(X) → π1(X). Does this involve group theory? It's supposed to be simple but I honestly I don't see how. Again, any help is greatly appreciated. Thanks.

Here is what the problem looks like. The thing is I don't remember what π1is exactly and I don't really know much group theory or know what equivalence classes are. I remember learning some group theory fact that f*(n) = n*f*(1). So, I think (a) was just equal to m since f(1) = 1 and (b) was...

I mean I have to use logic notation and probably some ideas from set theory to rigorously prove this is the case

I know that, I'm just having some trouble showing the equivalency of problem (a)

I included this image because it is easier than typing it out. Anyway, this is an old problem I need to catch up on. I have a clue as to how to do part a. I could say given an x that is a member of ∩V(Ai) which implies that x is a member of V(Ai) for ∀i. Then we can say ∀i all polynomials are in...

I don't really understand how unioning two numbers 0 and 1 makes a closed interval.

Basically with this problem, I need to show that f is continuous if A and B are open and if A and B are closed. My initial thoughts are that in the first case X must be open since unions of open sets are open. My question is that am I allowed to assume open sets exist in Y? Because then I can...

Yeah I mean an epsilon-delta proof that tan and arctan are continuous.

So, I already have a function in mind: tan(pi*x - pi/2) that maps (0, 1) to (0, oo). I just forget how to rigorously show that a function is continuous. I was hoping to get some help on showing that this tangent function I just wrote is continuous (not the topological definition, just like the...

so for the example you just gave, would I need to find a function that maps R \ {0} to (-3, -1) U (1,3)? I'm not very well versed in homeomorphism proofs

As I said in the summary, I don't really know how to even figure out which function would be appropriate to map the two sets that I described in the title. I'm using the book called Basic Topology by M.A. Armstrong. The book can sometimes be really dense. I am having a really hard time knowing...

I've pieced it together now. Thank you!

Yeah, it stands for "and."