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:

Shape fibration, multivalued map, homotopy groups, shape, groups, strong shape groups Shape fibration, multivalued map, homotopy groups, shape, groups, strong shape groups

MSC Classifications:

54C56, 55P55, 55Q05, 55Q07, 55R05 show english descriptions Shape theory [See also 55P55, 57N25]
Shape theory [See also 54C56, 55Q07]
Homotopy groups, general; sets of homotopy classes
Shape groups
Fiber spaces 54C56 - Shape theory [See also 55P55, 57N25]
55P55 - Shape theory [See also 54C56, 55Q07]
55Q05 - Homotopy groups, general; sets of homotopy classes
55Q07 - Shape groups
55R05 - Fiber spaces

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