James Tauber's Blog 2005/06/03
Atom Publishing Protocol
Dave Johnson of Roller fame has a great post outlining how the Atom Publishing Protocol will work.
I've commented before that I'd like to support blog clients in Leonardo and felt that a REST style made this much more straightforward.
Fortunately, Atom Publishing Protocol (APP), shares a very similar model to Leonardo so it looks like adding APP support to Leonardo will be fairly easy.
Also, the next version of Leonardo (discounting any bug releases) will switch to supporting the final version of the Atom feed format (assuming it's done in time, which it should be).
by jtauber : Created on June 3, 2005 : Last modified June 7, 2005 : Categories atompub leonardo : (permalink)
Homotopy
Consider two paths in the same topological space, X. Let's say one is the image of the map f from the interval [0, 1] and the other is the image of the map g from the interval [0, 1].
If it's possible to continuously deform f to g the two are said to be homotopic.
If x is the parameter for a path and t is the parameter for the deformation then we can think of the deformation as a continuous map F : [0, 1] x [0, 1] -> X where
- F(x, 0) = f(x)
- F(x, 1) = g(x)
and F(x, t) for some t, 0 < t < 1 is a path somewhere along in the deformation from f to g.
F is referred to as a homotopy from f to g.
Homotopies, as we shall soon see, will turn out to be a key to the topological difference between a sphere and a torus and will form the basis for our description of the Poincaré Conjecture itself.
UPDATE: next post
by jtauber : Created on June 3, 2005 : Last modified June 3, 2005 : Categories poincare_project : 0 comments (permalink)