Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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Gf-SPACES FOR MAPS AND POSTNIKOV SYSTEMS

  • Yoon, Yeon Soo (Department of Mathematics Education, Hannam University)
  • Received : 2009.11.03
  • Accepted : 2009.11.24
  • Published : 2009.12.30
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Abstract

For a map f : A $\rightarrow$ X, we define and study a concept of $G^f$-space for a map, which is a generalized one of a G-space. Any G-space is a $G^f$-space, but the converse does not hold. In fact, $S^2$ is a $G^{\eta}$-space, but not G-space. We show that X is a $G^f$-space if and only if $G_n$(A, f,X) = $\pi_n(X)$ for all n. It is clear that any $H^f$-space is a $G^f$-space and any $G^f$-space is a $W^f$-space. We can also obtain some results about $G^f$-spaces in Postnikov systems for spaces, which are generalization of Haslam's results about G-spaces.

Keywords

Acknowledgement

Supported by : Hannam University

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