In this paper, we introduce and study a new topology related to a self mapping on a nonempty set.Let X be a nonempty set and let f be a self mapping on X. Then the set of all invariant subsets ofX related to f, i.e. f := fA X : f(A) Ag P(X) is a topology on X. Among other things,we nd the smallest open sets contains a point x 2 X. Moreover, we find the relations between fand To f . For insta...

The polytope algebra is the universal group for translation invariant valuations on the family of polytopes in a nite dimensional vector space over an ordered eld. In an earlier paper, it was shown that the polytope algebra is, in all but one trivial respect, a graded (commutative) algebra over the base eld. Also described was a family of separating (group) homomorphisms, called frame functiona...