@Jonas: Geometry: think of the map admitting a section as a projection, and of the pre-images of the points as fibres. The graph of the section cuts each fiber in exactly one point.
Draw a picture of the projection of the unit square onto [0,1]
In the theory of fiber bundles, you always have local sections, and you can patch them together locally, but it may not be possible globally. That's one way to look at cohomology: obstructions of patching local sections together to a global one.
I thought at one point Stein wrote Toeplitz as Töplitz. Now I only see Toeplitz. Am I imagining or is the name really Töplitz, and just Anglicized for ASCII to Toeplitz?
@robjohn: right, oe is an alternative spelling for ö. Usually ö is used, unless you don't have the characters, but in names you don't do that. So there are people called Naef and people called Näf, different names, really.
@tb I was just wondering if Toeplitz had been spelled that way for so long due to lack of ö that it stuck, or whether it was originally that way. Anyway, I'm off for a bit.
@tb since the quotient topology on Y given X and surjection f:X->Y defined as U\subset Y is open iff f^{-1}(U) is open in X, any quotient map f is open and continuous, right?
a, no. not any open set can be presented as a pre-image
@JM: Yes and no. I am planning on making a very nice version of that, but have not. Our textbook has basic pictures, and a flowchart for identification, but in many ways is suboptimal. Let me dig up my current best resources, but they all lack something.
@JM: no problem. Yeah, I bring "polydrons" to class too, so they can see the 3d point groups. I really like helping them discover the 180 degree rotation of the tetrahedron.
Ah, I have the "tetrahedron in a cube" prepared for precisely that situation. :) I've had trouble explaining that rotation to people until I decided to make that model...
@JonasTeuwen we have a server and just set up a repository as if it were on a local computer there. Mercurial takes care of the rest (as far as I understand it)
back in my homological algebra days I used "xymatrix" in the xypic (or xy) package. I haven't tried using tikz for commutative diagrams, but I use it all the time for pictures
yeah, i am very impressed they (xy and tikz) managed to write a compiler in tex for a new language, but like most early generation compilers, the error message should probably just say "I am only a machine, please help me!"
@tb how do you tell which comment that is? firefox and safari are both removing the #comment thing from the url
haha
guess it doesn't matter, that isn't a very nice thread at all
is there any way to see what posts you've downvoted? i tried to write a query on the data.se site, but apparently i don't have permission to view my votes
