Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지

G'-SEQUENCE OF A MAP

  • Yoon, Yeon Soo (Department of Mathematics Education, Hannam University)
  • Received : 2008.12.15
  • Accepted : 2009.02.13
  • Published : 2009.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

Pan, Shen and Woo [8] introduced the concept of the G-sequence of a map. We introduce the G'-sequence of a map, which is a dual concept of the G-sequence of a map. We obtain some sufficient conditions for the all sets in the G'-sequence of a map are groups, and for the exact G'-sequence of a map.

Keywords

Acknowledgement

Supported by : Hannam University

References

  1. D. H. Gottlieb, A certain subgroup of the fundamental group, Amer. J. Math. 87 (1965), 840-856. https://doi.org/10.2307/2373248
  2. D. H. Gottlieb, Evaluation subgroups of homotopy groups, Amer. J. Math. 91 (1969), 729-756. https://doi.org/10.2307/2373349
  3. H. B. Haslam, G-spaces and H-spaces, Ph. D. Thesis, Univ. of California, Irvine, 1969.
  4. P. Hilton, Homotopy Theory and Duality, 1965.
  5. K. L. Lim, Cocyclic maps and coevaluation subgroups, Canad. Math. Bull. 30 (1987), 63-71. https://doi.org/10.4153/CMB-1987-009-1
  6. R. E. Mosher and M. C. Tangora, Cohomology operations and applications in homotopy theory, Harper & Row, New York, 1968.
  7. N. Oda, The homotopy of the axes of pairings , Canad. J. Math. 17 (1990), 856-868.
  8. J. Z. Pan and X. Shen and M. H. Woo, The G-sequence of a map and its exactness, J. Korean Math. Soc. 35 (1998), no. 2, 281-294.
  9. K. Varadarajan, Genralized Gottlieb groups, J. Indian Math. Soc. 33 (1969), 141-164.
  10. M. H. Woo and K. Y. Lee, On the relative evaluation subgroups, J. Korean Math. Soc. 25 (1988), no. 1, 149-160.
  11. M. H. Woo and Y. S. Yoon, T-spaces by the Gottlieb groups and duality, J. Austral. Math. Soc., (Series A) 59 (1995), 193-203. https://doi.org/10.1017/S1446788700038593
  12. Y. S. Yoon, The generalized dual Gottlieb sets, Top. Appl. 109 (2001), 173-181. https://doi.org/10.1016/S0166-8641(99)00150-9
  13. Y. S. Yoon, $H^{f}$-spaces for maps and their duals, J. Korea Soc. Math. Educ. Ser. B Vol. 14(4) (2007), 289-306.
  14. A. Zabrodsky, Hopf spaces , North-Holland Publishing com., 1976.