# G'p-SPACES FOR MAPS AND HOMOLOGY DECOMPOSITIONS

• Yoon, Yeon Soo
• Accepted : 2015.10.26
• Published : 2015.11.15
• 23 1

#### 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