Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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PRINCIPAL FIBRATIONS AND GENERALIZED H-SPACES

  • Yoon, Yeon Soo (Department of Mathematics Education, Hannam University)
  • Received : 2016.01.19
  • Accepted : 2016.02.05
  • Published : 2016.02.15
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Abstract

For a map $f:A{\rightarrow}X$, there are concepts of $H^f$-spaces, $T^f$-spaces, which are generalized ones of H-spaces [17,18]. In general, Any H-space is an $H^f$-space, any $H^f$-space is a $T^f$-space. For a principal fibration $E_k{\rightarrow}X$ induced by $k:X{\rightarrow}X^{\prime}$ from ${\epsilon}:PX^{\prime}{\rightarrow}X^{\prime}$, we obtain some sufficient conditions to having liftings $H^{\bar{f}}$-structures and $T^{\bar{f}}$-structures on $E_k$ of $H^f$-structures and $T^f$-structures on X respectively. We can also obtain some results about $H^f$-spaces and $T^f$-spaces in Postnikov systems for spaces, which are generalizations of Kahn's result about H-spaces.

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References

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