The sheaf of the groups formed by H-Cogroups over topological spaces

Authors : Aa ÖÇAL

Pages : 0-0

Doi:10.1501/Commua1_0000000553

View : 11 | Download : 13

Publication Date : 1988-01-01

Article Type : Research Paper

Abstract :In thio paper, we consider both homotopy and sheaf theory and construct an algebraic sheaf by means of the H-cogroups. Finally, we give some algebraic topological characterizations. 1. The Sheaf of the Groups formed by H-Cogroups över topological spaces. ‘ Lct’s recall the following definition, Definition 1.1. Let S be two topological spaces, and tz: S X be a locally topological map. Then the pair insert ignore into journalissuearticles values(S, k); or shortly S is c aile d a sheaf över X. Let insert ignore into journalissuearticles values(5 be the category of topological spaces X satisfying the pro- perty that ali pointed topological spaces insert ignore into journalissuearticles values(X,x); with x e İL have the same homotopy type. This category inciudes for example ali topological vector spaces. Let us take xeinsert ignore into journalissuearticles values(5 as a base set if Q is any H-cogroup, then the set of homotopy class of homotop maps preserving the base points from insert ignore into journalissuearticles values(Q,qo); to insert ignore into journalissuearticles values(X,Xi);, iel, [Q; insert ignore into journalissuearticles values(X,Xi);] obtained for each xeX, insert ignore into journalissuearticles values(X,x); pointed topological spaces. i.e, Pinsert ignore into journalissuearticles values(X); = V [Q; insert ignore into journalissuearticles values(X,x);]. Thus Pinsert ignore into journalissuearticles values(X); is a set över
Keywords : sheaf, groups formed, H Cogroups