Hostname: page-component-cb9f654ff-k7rjm Total loading time: 0 Render date: 2025-08-23T23:55:01.801Z Has data issue: false hasContentIssue false
  • English
  • Français

Shape Fibrations, Multivalued Maps and Shape Groups

Published online by Cambridge University Press:  20 November 2018

Antonio Giraldo
Antonio Giraldo*
Affiliation:
Departamento de Matemática Aplicada Facultad de Informática Universidad Politécnica Campus de Montegancedo Boadilla del Monte, 28660 Madrid Spain, e-mail: agiraldo@fi.upm.es
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The notion of shape fibration with the near lifting of near multivalued paths property is studied. The relation of these maps—which agree with shape fibrations having totally disconnected fibers—with Hurewicz fibrations with the unique path lifting property is completely settled. Some results concerning homotopy and shape groups are presented for shape fibrations with the near lifting of near multivalued paths property. It is shown that for this class of shape fibrations the existence of liftings of a fine multivalued map is equivalent to an algebraic problem relative to the homotopy, shape or strong shape groups associated.

Keywords

54C5655P5555Q0555Q0755R05Shape fibrationmultivalued maphomotopy groupsshape groupsstrong shape groups

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 50 , Issue 2 , 01 April 1998 , pp. 342 - 355
Copyright
Copyright © Canadian Mathematical Society 1998

References

1. Bing, R.H., Concerning hereditarily indecomposable continua. Pacific J. Math. 1(1951), 43–51.Google Scholar
2. Čerin, Z., Equivalence of approximate fibrations and shape fibrations. Topology Appl. 76(1997), 9–26.Google Scholar
3. Coram, D. and Duvall, P.F., Jr, Approximate fibrations. Rocky Mountain J. Math. 7(1977), 275–288.Google Scholar
4. Giraldo, A. and R, J.M.. Sanjurjo, Strong multihomotopy and Steenrod loop spaces. J. Math. Soc. Japan. 47(1995), 475–489.Google Scholar
5. Lacher, R.C., Cellularity criteria for maps. Michigan Math. J. 17(1970), 385–396.Google Scholar
6. Lacher, R.C., Cell-like maps and their generalizations. Bull. Amer.Math. Soc. 83(1977), 495–552.Google Scholar
7. Mardešić, S., Approximate polyhedra, resolutions of maps and shape fibrations. Fund. Math. 114(1981), 53–78.Google Scholar
8. Mardešić, S. and Rushing, T.B., Shape fibrations. Gen. Topology Appl. 9(1978), 193–215.Google Scholar
9. Mardešić, S., Shape fibrations II. Rocky Mountain J. Math. 9(1979), 283–298.Google Scholar
10. R, J.M.. Sanjurjo, Multihomotopy sets and transformations induced by shape. Quart. J. Math. Oxford Ser. (2) 42(1991), 489–499.Google Scholar
11. Sanjurjo, J.M.R., An intrinsic description of shape. Trans. Amer.Math. Soc. 329(1992), 625–636.Google Scholar
12. R, J.M.. Sanjurjo, Multihomotopy, Čech spaces of loops and shape groups. Proc. LondonMath. Soc. (3) 69(1994), 330–344.Google Scholar