DERIVED LIMITS AND GROUPS OF PURE EXTENSIONS

  • LEE, H.J. (Dept. of Mathematics, Chonbuk National University) ;
  • KIM, S.J. (Dept. of Mathematics, Chonbuk National University) ;
  • HAN, Y.H. (Dept. of Mathematics, Chonbuk National University) ;
  • LEE, W.H. (Dept. of Mathematics, Chonbuk National University) ;
  • LEE, D.W. (Dept. of Mathematics, Chonbuk National University)
  • Received : 1999.05.10
  • Published : 1999.07.30

Abstract

For a k-connected inverse system $({\scr{X}},\;*)=((X_{\lambda},\;*),p_{{\lambda}{{\lambda}}^{\prime}},\;{\Lambda})$ of pointed topological spaces and pointed preserving weak fibrations, inducting epimorphic chain maps, over a directed set, we show that the homotopy group ${\pi}_k(lim{\scr{X}},\;*)$ of the inverse limit is isomorphic to the integral homology group $$H_k(lim{\scr{X}};\mathbb{Z})$. Using the result of S. $Marde{\check{s}}i{\acute{c}}$, we prove that the group of pure extension $Pext(colimH^n({\scr{X}},\;A)$ is isomorphic to the group of extension $Ext({\Delta}({\lambda}),\;Hom(H^n({\scr{X}}),\;A))$.

Keywords

derived limit;pure extension;shape group;${\check{C}ech$ homology group;${\kappa}$-connectivity

Acknowledgement

Supported by : Chonbuk National University

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