Recent content by redbowlover

thanks...i'll think about this

for me a proper map is a continuous map such that the preimage of a compact set is compact. Unfortunately there is no extra conditions on X. and since I've never worked with nets before, a net-free solution would be best :-) I went with a sequence route because I know it works for proper...

My quick question is this: I know it's true that any sequence in a compact metric space has a convergent subsequence (ie metric spaces are sequentially compact). Also, any arbitrary compact topological space is limit point compact, ie every (infinite) sequence has a limit point. So in general...

thanks..trying to lift some paths helped me see why what i was doing didn't make sense. the map i had in mind couldn't be a covering map bc there would be no evenly covered nbhd of the vertex of the figure-8. oops :-)

Ok so apparently the universal cover of the figure-8 can be represented by the cayley graph of the free group on two generators, discussed in Hatcher and here http://en.wikipedia.org/wiki/Rose_%28topology%29" i can see why this is a universal cover of the figure-8. but I'm having trouble...

thanks!

Working through Hatcher... For any space X, we have an augmented chain complex ...\rightarrow C_1(X) \rightarrow C_0(X)\rightarrow \mathbb{Z}\stackrel{\epsilon}{\rightarrow}0 Hathcer says that since \epsilon induces a map H_0(X)\rightarrow \mathbb{Z} with kernel \tilde{H}_0(X), we get an...

Hello, Looking through Torchinksy's Real Variables text and I'm infinitely confused about convolutions. For two integrable functions f, g \in \ L^1(R) we define the convolution f*g=\int_R f(x-y)g(y) dy , \forall x\in R . Then, apparently, f*g is also integrable. But I'm not sure how...

tex doesn't seem to be working right...sry for the notation. Working through of a proof of the generalized jordan curve theorem. Keep getting stuck on calculating the reduced homology of S^n by R, (ie n-sphere cross the real line). My book (hatcher) seems to imply its 0 except the n^th...

i may be mistaken but i don't think the position of the points matters that much. if you start with any (nice) array of points you can connect them to create the pattern... for example, draw a point and then draw 5 points around in. connect each of the outside points to the center and each...

i'm curious about the context of the question. a solid handle by itself is contractible and so mathematicians wouldn't bother giving it a name. but we often refer to "handles" when we are attaching them to other spaces. a coffee cup handle would be a 3-handle...if you attached a 3-handle to a...

your post was extremely enlightening, thank you. although i kind of lost jarle and you in posts following :-)

Yes, there are examples of functions that are Riemann integrable but not Lebesgue integrable but my question is about functions that are not Riemann integrable.

I do recall that theorem. But what if the function is not bounded? For example, define f to be 1/x on (0,1] and 0 at 0. Then clearly f is not Riemann integrable. It would seem intuitively true that its not Lebesgue integrable.

Right, ok. I guess I was thinking about this in a specific way. Let's see. Are their conditions that can be set to change this? For example if a function is continuous almost everywhere on a domain but not Riemann integrable, can it be Lebesgue integrable?