On Fundamental Approximative Absolute Neighborhood Retracts
Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 134-142

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we define and study a class of compacta under the name of Fundamental Approximative Absolute Neighborhood Retracts. This class includes Borsuk’s Fundamental Absolute Neighborhood Retracts and Approximative Absolute Neighborhood Retracts in the sense of M. H. Clapp as proper subclasses. We also introduce the notion of q-strong movability and prove that Fundamental Approximative Absolute Neighborhood Retracts coincide with q-strongly movable compacta.
Sanjurjo, J. M. R. On Fundamental Approximative Absolute Neighborhood Retracts. Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 134-142. doi: 10.4153/CMB-1984-021-8
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[1] 1. Bogatyĭ, S. A., Approximative and fundamental retracts, Math. USSR Sbornik, 22 (1974), 91–103. Google Scholar

[2] 2. Borsuk, K., Fundamental retracts and extensions of fundamental sequences, Fund. Math. 64 (1969), 55–85. Google Scholar

[3] 3. Borsuk, K., Theory of Shape, Lecture Notes Series No. 28, Matematisk Inst. Aarhus University 1971, 1–145. Google Scholar

[4] 4. Borsuk, K., Theory of Shape, Monografie Matematyczne 59. PWN-Polish Scientific Publishers, Warszawa, 1975. Google Scholar

[5] 5. Borsuk, K., On a class of compacta, Houston J. Math. 1 (1975), 1–13. Google Scholar

[6] 6. Čerin, Z., -E-movable and -E-calm compacta and their images, Compositio Math. 45 (1981), 115–141. Google Scholar

[7] 7. Čerin, , ANR’s, Z. and AANR’s revisited, Lecture given at the Conference on Shape Theory and Geometric Top. Dubrovnik. Yugoslavia 1981. Google Scholar

[8] 8. Clapp, M. H., On a generalization of absolute neighborhood retracts, Fund. Math. 70 (1971), 117–130. Google Scholar

[9] 9. Cox, C., Three questions of Borsuk concerning movability and fundamental retraction, Fund. Math. 80 (1973), 169–179. Google Scholar

[10] 10. Dydak, J. and Segal, J., Shape Theory. An introduction, Lecture Notes in Mathematics, 688. Springer Verlag (1978). Google Scholar

[11] 11. Gmurczyk, A., On approximative retracts, Bull. Acad. Polon. Sci, 16 (1968), 9–14. Google Scholar

[12] 12. Gmurczyk, A., Approximative retracts and fundamental retracts, Colloq. Math, 23 (1971), 61–63. Google Scholar

[13] 13. Granas, A., Fixed point theorems for the approximative ANR’s, Bull. Acad. Polon. Sci. 16 (1968), 15–19. Google Scholar

[14] 14. Hu, S. T., Theory of retracts, Wayne State University Press. Detroit, 1965. Google Scholar

[15] 15. Kalinin, V. A., Approximating retracts for classes of bicompact spaces, Siberian Math. J. 16 (1975), 553–562. Google Scholar

[16] 16. Mardešić, S., Shapes for topological spaces, General Topology Appl. 3 (1973), 265–282. Google Scholar

[17] 17. Mardešić, S., Approximate Polyhedra, resolutions of maps and shape fibrations, Fund. Math. 114 (1981), 53–78. Google Scholar

[18] 18. Noguchi, H., A generalization of absolute neighborhood retracts, Kodai. Math. Seminar Reports 1 (1953), 20–22. Google Scholar

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