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