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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
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Abstract

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

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