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G'p-SPACES FOR MAPS AND HOMOLOGY DECOMPOSITIONS

  • Yoon, Yeon Soo
  • Received : 2015.09.16
  • Accepted : 2015.10.26
  • Published : 2015.11.15

Abstract

For a map $p:X{\rightarrow}A$, we define and study a concept of $G^{\prime}_p$-space for a map, which is a generalized one of a G'-space. Any G'-space is a $G^{\prime}_p$-space, but the converse does not hold. In fact, $CP^2$ is a $G^{\prime}_{\delta}$-space, but not a G'-space. It is shown that X is a $G^{\prime}_p$-space if and only if $G^n(X,p,A)=H^n(X)$ for all n. We also obtain some results about $G^{\prime}_p$-spaces and homology decompositions for spaces. As a corollary, we can obtain a dual result of Haslam's result about G-spaces and Postnikov systems.

Keywords

$G^f$-spaces for maps;Postnikov systems

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Acknowledgement

Supported by : Hannam University