Subject: from darush.aghababayeedehkordi(generalized homotopy theory)
From: "darush aghababayeedehkordi"
Date: Tue, 19 Jun 2007 17:06:45 +0330
dear all
i introduce generalized homotopy theory of topological spaces
let X, Y are any paire of topological space such that there a continuouse
function H from cartesian product of X and I to Y such that H(x,t) =f(x)
and H(x,1-t)=g(x) in a special case t=0 H is a homotopy between X ,Y .
so that we imply every homotopy is a generalized homotop but its converes
not true.
Subject: from darush.aghabbayeedehkordi( hyperhomotopy of topological
spaces)
From: "darush aghababayeedehkordi"
Date: Tue, 19 Jun 2007 17:18:00 +0330
let X, Y are any paire of topological space and * is a hyper operation on
Y in this case we define hyper homotopy of X,Y :
H from cross product of X, I and P(Y) such that *H(x,0)=f(x)*f(x) and
*H(x,1)= g(x)*g(x)
such that f,g are super continuouse multifunctions.
in a special case if i have a homotopy H between X,Y let *H(x,0)
=H(x,0)*H(x,0) , *H(x,1)=H(x,1)*H(x,1)
we have a hyper homotopy
corollary : every homotopy is a hyper hmotopy.
we can rename hyper homotopy as a homotopy of" super continuouse
multifunctions"
Subject: from darush.aghababayeedehkordi( genralized hyperhomotopy)
From: "darush aghababayeedehkordi"
Date: Tue, 19 Jun 2007 17:22:41 +0330
dear all
in a definition of hyper homotopy replace zero with t and 1 with 1-t
in this case we have a generalized hyperhomotopy .
every hyper homotopy is a hyperformulas in classification theory.
P(Y) means power set on Y
every function from cartesian productt Y,Y to P(Y) is a hyper operation
every operation is a hyper operation.
*H(x,t)= * o H(x,t) because * is a function