Strong multihomotopy and Steenrod loop spaces

Antonio GIRALDO; Jose M. R. SANJURJO

doi:10.2969/jmsj/04730475

Antonio GIRALDO, Jose M. R. SANJURJO

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JOURNAL FREE ACCESS

1995 Volume 47 Issue 3 Pages 475-489

DOI https://doi.org/10.2969/jmsj/04730475

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Published: 1995 Received: October 21, 1993 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) F. W. Bauer, A shape theory with singular homology, Pacific J. Math., 64 (1976), 25-65.
2) K. Borsuk, Theory of shape, Monografie Matematyczne, 59, Polish Scientific Publishers, Warszawa, 1975.
3) F. W. Cathey, Strong shape theory, In Shape Theory and Geom. Top. Proc., Dubrovnik 1981, (eds. S. Mardešic and J. Segal), Lecture Notes in Math., 870, Springer-Verlag, Berlin, 1981, pp. 215-238.
4) Z. Cerin and T. Watanabe, Borsuk fixed point theorem for multivalued maps, In Geometric Topology and Shape Theory, (eds. S. Mardešic and J. Segal), Lecture Notes in Math., 1283, Springer-Verlag, Berlin, 1987, pp. 30-37.
5) T. A. Ghapman, On some applications of infinite-dimensional manifolds to the theory of shape, Fund. Math., 76 (1972), 191-193.
6) D. Christie, Net homotopy for compacta, Trans. Amer. Math. Soc., 56 (1944), 275-308.
7) J. M. Cordier and T. Porter, Shape theory, Categorical methods of approximation, Ellis Horwood Series: Mathematics and its applications, Ellis Horwood Ltd., Chichester, 1989.
8) J. Dydak and J. Segal, Shape theory, An introduction, Lecture Notes in Math., 688, Springer-Verlag, Berlin, 1978.
9) J. Dydak and J. Segal, Strong shape theory, Dissertationes Math., 192 (1981), 1-42.
10) J. Dydak and J. Segal, A list of open problems in shape theory, In Open problems in Topology, (eds. J. V. Mills and G. M. Reed), North Holland, 1990, pp. 457-467.
11) D. A. Edwards and H. M. Hastings, Cech and Steenrod homotopy theories with applications to geometric topology, Lecture Notes in Math., 542, Springer-Verlag, Berlin, 1976.
12) H. M. Hastings, Steenrod homotopy theory, homotopy idempotents and homotopy limits, Topology Proc., 2 (1977), 461-476.
13) Y. Kodama, Multivalued maps and shape, Glasnik Mat., 12 (1977), 133-142.
14) Y. Kodama and J. Ono, On fine shape theory I, Fund. Math., 105 (1979), 29-39.
15) Y. Kodama and J. Ono, On fine shape theory II, Fund. Math., 108 (1980), 89-98.
16) A. Koyama, Various compact multi-retracts and shape theory, Tsukuba J. Math., 6 (1982), 319-332.
17) S. Mardešic and J. Segal, Shape theory, Mathematical library, 26, North Holland, Amsterdam, 1982.
18) T. Porter, Cech homotopy, J. London Math. Soc., 6 (1973), 429-436.
19) J. B. Quigley, An exact sequence from the nth to the (n-1)th fundamental group, Fund. Math., 77 (1973), 195-210.
20) J. M. R. Sanjurjo, An intrinsic description of shape, Trans. Amer. Math. Soc., 329 (1992), 625-636.
21) J. M. R. Sanjurjo, Multihomotopy sets and transformations induced by shape, Quart. J. Math. Oxford (2), 42 (1991), 489-499.

Right : [1] F. W. Bauer, A shape theory with singular homology, Pacific J. Math., 64 (1976), 25-65.
[2] K. Borsuk, Theory of shape, Monografie Matematyczne, 59, Polish Scientific Publishers, Warszawa, 1975.
[3] F. W. Cathey, Strong shape theory, In Shape Theory and Geom. Top. Proc., Dubrovnik 1981, (eds. S. Mardešic and J. Segal), Lecture Notes in Math., 870, Springer-Verlag, Berlin, 1981, pp. 215-238.
[4] Z. Cerin and T. Watanabe, Borsuk fixed point theorem for multivalued maps, In Geometric Topology and Shape Theory, (eds. S. Mardešic and J. Segal), Lecture Notes in Math., 1283, Springer-Verlag, Berlin, 1987, pp. 30-37.
[5] T. A. Ghapman, On some applications of infinite-dimensional manifolds to the theory of shape, Fund. Math., 76 (1972), 191-193.
[6] D. Christie, Net homotopy for compacta, Trans. Amer. Math. Soc., 56 (1944), 275-308.
[7] J. M. Cordier and T. Porter, Shape theory, Categorical methods of approximation, Ellis Horwood Series: Mathematics and its applications, Ellis Horwood Ltd., Chichester, 1989.
[8] J. Dydak and J. Segal, Shape theory, An introduction, Lecture Notes in Math., 688, Springer-Verlag, Berlin, 1978.
[9] J. Dydak and J. Segal, Strong shape theory, Dissertationes Math., 192 (1981), 1-42.
[10] J. Dydak and J. Segal, A list of open problems in shape theory, In Open problems in Topology, (eds. J. V. Mills and G. M. Reed), North Holland, 1990, pp. 457-467.
[11] D. A. Edwards and H. M. Hastings, Cech and Steenrod homotopy theories with applications to geometric topology, Lecture Notes in Math., 542, Springer-Verlag, Berlin, 1976.
[12] H. M. Hastings, Steenrod homotopy theory, homotopy idempotents and homotopy limits, Topology Proc., 2 (1977), 461-476.
[13] Y. Kodama, Multivalued maps and shape, Glasnik Mat., 12 (1977), 133-142.
[14] Y. Kodama and J. Ono, On fine shape theory I, Fund. Math., 105 (1979), 29-39.
[15] Y. Kodama and J. Ono, On fine shape theory II, Fund. Math., 108 (1980), 89-98.
[16] A. Koyama, Various compact multi-retracts and shape theory, Tsukuba J. Math., 6 (1982), 319-332.
[17] S. Mardešic and J. Segal, Shape theory, Mathematical library, 26, North Holland, Amsterdam, 1982.
[18] T. Porter, Cech homotopy, J. London Math. Soc., 6 (1973), 429-436.
[19] J. B. Quigley, An exact sequence from the nth to the (n-1)th fundamental group, Fund. Math., 77 (1973), 195-210.
[20] J. M. R. Sanjurjo, An intrinsic description of shape, Trans. Amer. Math. Soc., 329 (1992), 625-636.
[21] J. M. R. Sanjurjo, Multihomotopy sets and transformations induced by shape, Quart. J. Math. Oxford (2), 42 (1991), 489-499.

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