RT Journal Article
T1 Multifibrations. A class of shape fibrations with the path lifting property
A1 Giraldo, A.
A1 Rodríguez Sanjurjo, José Manuel
AB In this paper we introduce a class of maps possessing a multivalued homotopy lifting property with respect to every topological space. We call these maps multifibrations and they represent a formally stronger concept than that of shape fibration. Multifibrations have the interesting property of being characterized in a completely intrinsic. way by a path lifting property involving only the total and the base space of the fibration. We also show that multifibrations land also, with some restrictions, shape fibrations) have a lifting property for homotopies of fine multivalued maps. This implies, when the spaces considered are metric compacta, that the possibility of lifting a fine multivalued map is a property of the corresponding strong shape morphism and not of the particular map considered.
PB Mathematical Institute of the Academy of Sciences of the Czech Republic
SN 1572-9141
YR 2001
FD 2001
LK https://hdl.handle.net/20.500.14352/57655
UL https://hdl.handle.net/20.500.14352/57655
LA eng
NO K. Borsuk: On movable compacta. Fund. Math. 66 (1969), 137–146.K. Borsuk: Theory of Shape (Monografie Matematyczne 59). Polish Scientific Publishers, Warszawa, 1975.F.W.Cathey: Shape fibrations and strongs hape theory. Topology Appl. 14 (1982), 13–30.Z . Čerin: Shape theory intrinsically. Publ. Mat. 37 (1993), 317–334.Z . Čerin: Proximate topology and shape theory. Proc. Roy. Soc. Edinburgh 125 (1995), 595–615.Z . Čerin: Approximate fibrations. To appear.D. Coram and P. F. Duvall, Jr.: Approximate fibrations. Rocky Mountain J. Math. 7 (1977), 275–288.J.M.Cordier and T. Porter: Shape Theory. Categorical Methods of Approximation (Ellis Horwood Series: Mathematics and its Applications). Ellis Horwood Ltd., Chichester, 1989.J. Dydak and J. Segal: Shape Theory: An Introduction (Lecture Notes in Math. 688). Springer-Verlag, Berlin, 1978.J. Dydak and J. Segal: A list of open problems in shape theory. J.Van Mill and G. M.Reed: Open problems in Topology. North Holland, Amsterdam, 1990, pp. 457–467.J. E. Felt: ε-continuity and shape. Proc. Amer. Math. Soc. 46 (1974), 426–430.A. Giraldo: Shape fibrations, multivalued maps and shape groups. Canad. J. Math 50 (1998), 342–355.A. Giraldo and J. M. R. Sanjurjo: Strongm ultihomotopy and Steenrod loop spaces. J. Math. Soc. Japan. 47 (1995), 475–489.R.W. Kieboom: An intrinsic characterization of the shape of paracompacta by means of non-continuous single-valued maps. Bull. Belg. Math. Soc. 1 (1994), 701–711.K. Kuratowski: Topology I. Academic Press, New York, 1966.S. Mardešic: Approximate fibrations and shape fibrations. Proc. of the International Conference on Geometric Topology. PWN, Polish Scientific Publishers, 1980, pp. 313–322.S. Mardešic and T.B.Rushing: Shape fibrations. General Topol. Appl. 9 (1978), 193–215.S. Mardešic and T.B.Rushing: Shape fibrations II. Rocky Mountain J. Math. 9 (1979), 283–298.S. Mardešic and J. Segal: Shape Theory. North Holland, Amsterdam, 1982.E.Michael: Topologies on spaces of subsets. Trans. Amer. Math. Soc. 71 (1951), 152–182.M. A.Morón and F. R.Ruiz del Portal: Multivalued maps and shape for paracompacta. Math. Japon. 39 (1994), 489–500.J. M. R. Sanjurjo: A non-continuous description of the shape category of compacta. Quart. J. Math. Oxford (2) 40 (1989), 351–359.J. M. R. Sanjurjo: Multihomotopy sets and transformations induced by shape. Quart. J. Math. Oxford (2) 42 (1991), 489–499.J. M. R. Sanjurjo: An intrinsic description of shape. Trans. Amer. Math. Soc. 329 (1992), 625–636.J. M. R. Sanjurjo: Multihomotopy, Čech spaces of loops and shape groups. Proc. London Math. Soc. (3) 69 (1994), 330–344.
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