Recent content by tom.coyne

I thought about trying to use Whitehead's Theorem. But it states that if a map between CW complexes induces isomorphism on all homotopy groups then it is a homotopy equivalence. I wasn't sure how to use this though. Also, I am not sure I totally understood your previous answer. Were you...

If f\circ g \simeq f \circ h \; \Rightarrow \; g \simeq h then f_*\circ g_* = f_* \circ h_* \; \Rightarrow \; g_* = h_* hence f_* is injective. If f is a map such that f_* is monic for all homotopy groups, then if we have f \circ g \simeq f \circ h then this implies that f_* \circ g_* = f_*...

Ok, so if f is an injection into a contractible space Y then if g \not\simeq h then we would still have f \circ g \simeq f \circ h. Thanks!

So if f is a split monomorphism then this works. What about when its not a split monomorphism? Can you think of any counter examples?

Hi, I know that if I have a monomorphism f:X\rightarrow Y then for any arrows g,h:A \rightarrow X we have f \circ g = f \circ h \; \Rightarrow \; g=h However in a topological space, if I have f to be an injection but now have f \circ g \simeq f \circ h (where \simeq denotes homotopic) then...

How am I going to make sure that the points remain next to each other? I can see that it would be easy for a line, but it gets more complex for a circle. Then my aim is to make quite complex snake like shapes. Since I will be integrating this data, it would be best if the data points which...

Thanks for the tip, however after spending some time trawling the help pages, I'm still not sure how to proceed. So at the moment I have drawn a circle in paint and saved it as a greyscale bmp. imread will then turn this into a matrix of 1's and 0's. I take it these refer to the pixels a 1...

Hi, I am currently using MATLAB to do some work on simple closed curves in the plane. In order to make this work quite general I have opted to use a matrix which stores (x,y) coordinates of points on my curve (rather than use a function). I want to feed some interesting curves into my code...