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On Fundamental Approximative Absolute Neighborhood Retracts

Published online by Cambridge University Press:  20 November 2018

J. M. R. Sanjurjo
J. M. R. Sanjurjo*
Affiliation:
Facultad de Matemáticas, Universidad Complutense Madrid (3), Spain
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Abstract

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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.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 2 , 01 June 1984 , pp. 134 - 142
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Bogatyĭ, S. A., Approximative and fundamental retracts, Math. USSR Sbornik, 22 (1974), 91–103.Google Scholar
2. Borsuk, K., Fundamental retracts and extensions of fundamental sequences, Fund. Math. 64 (1969), 55–85.Google Scholar
3. Borsuk, K., Theory of Shape, Lecture Notes Series No. 28, Matematisk Inst. Aarhus University 1971, 1–145.Google Scholar
4. Borsuk, K., Theory of Shape, Monografie Matematyczne 59. PWN-Polish Scientific Publishers, Warszawa, 1975.Google Scholar
5. Borsuk, K., On a class of compacta, Houston J. Math. 1 (1975), 1–13.Google Scholar
6. Čerin, Z., -E-movable and -E-calm compacta and their images, Compositio Math. 45 (1981), 115–141.Google Scholar
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. Clapp, M. H., On a generalization of absolute neighborhood retracts, Fund. Math. 70 (1971), 117–130.Google Scholar
9. Cox, C., Three questions of Borsuk concerning movability and fundamental retraction, Fund. Math. 80 (1973), 169–179.Google Scholar
10. Dydak, J. and Segal, J., Shape Theory. An introduction, Lecture Notes in Mathematics, 688. Springer Verlag (1978).Google Scholar
11. Gmurczyk, A., On approximative retracts, Bull. Acad. Polon. Sci, 16 (1968), 9–14.Google Scholar
12. Gmurczyk, A., Approximative retracts and fundamental retracts, Colloq. Math, 23 (1971), 61–63.Google Scholar
13. Granas, A., Fixed point theorems for the approximative ANR’s, Bull. Acad. Polon. Sci. 16 (1968), 15–19.Google Scholar
14. Hu, S. T., Theory of retracts, Wayne State University Press. Detroit, 1965.Google Scholar
15. Kalinin, V. A., Approximating retracts for classes of bicompact spaces, Siberian Math. J. 16 (1975), 553–562.Google Scholar
16. Mardešić, S., Shapes for topological spaces, General Topology Appl. 3 (1973), 265–282.Google Scholar
17. Mardešić, S., Approximate Polyhedra, resolutions of maps and shape fibrations, Fund. Math. 114 (1981), 53–78.Google Scholar
18. Noguchi, H., A generalization of absolute neighborhood retracts, Kodai. Math. Seminar Reports 1 (1953), 20–22.Google Scholar