Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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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
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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

Acknowledgement

Supported by : Chonbuk National University

References

  1. Infinite abelian groups Fuchs, L.
  2. Comment Math. Helvetici v.53 Cohomology theories and infinite CW-complexes Huber, M.;Meier, W.
  3. Topology Appl. v.19 Strong homology of inverse system of spaces I,II Lisica, J.T.;Mardesic, S.
  4. Topology Appl. v.68 Strong homology does not have compact supports Mardesic, S.
  5. Topology v.35 no.2 Nonvanishing derived limits in shape theory Mardesic, S.
  6. Glasnik Mat. v.25 no.45 The relative homeomorphism and wedge axioms for strong homology Mardesic, S.;Miminoshvili, Z.
  7. Topology Appl. v.82 On strong homology of compact spaces Mardesic, S.;Prasolov, A.V.
  8. Shape theory Mardesic, S.;Segal, J.
  9. Phantom maps, Handbook of algebraic topology McGibbon, C.A.
  10. J. Pure Appl. Algebra v.103 Some questions about the first derived functor of the inverse limit McGibbon, C.A.;Steiner, R.
  11. Topology v.1 Uber die derivierten des inversen und des derekten limes einer modulefamile Nobeling, G.
  12. Trans. Amer. Math. Soc. v.132 Homological dimension and the continuum hypothesis Osofsky, B.L.
  13. Algebraic topology Spanier, E.
  14. Glasnik Mat. v.26 no.46 An elementary proof of the invariance of $lim^{(n)}$ pro-abe lain groups Watanabe, T.