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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.14 No.4

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Hf -Spaces for Maps and Their Duals

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2007, v.14 no.4, pp.289-306
Yoon, Yeon-Soo
Yoon,, Y. (2007). Hf -Spaces for Maps and Their Duals. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 14(4), 289-306.

Abstract

We define and study a concept of <TEX>$H^f-space$</TEX> for a map, which is a generalized concept of an H-space, in terms of the Gottlieb set for a map. For a principal fibration <TEX>$E_{\kappa}{\rightarrow}X$</TEX> induced by <TEX>${\kappa}:X{\rightarrow}X'\;from\;{\epsilon}:\;PX'{\rightarrow}X'$</TEX>, we can obtain a sufficient condition to having an <TEX>$H^{\bar{f}}-structure\;on\;E_{\kappa}$</TEX>, which is a generalization of Stasheff's result [17]. Also, we define and study a concept of <TEX>$co-H^g-space$</TEX> for a map, which is a dual concept of <TEX>$H^f-space$</TEX> for a map. Also, we get a dual result which is a generalization of Hilton, Mislin and Roitberg's result [6].

keywords
<tex> $H^f-space$</tex> for maps, <tex> $co-H^g-space$</tex> for maps

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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