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26. CJM 1998 (vol 50 pp. 342)

Giraldo, Antonio
Shape fibrations, multivalued maps and shape groups
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
Categories:54C56, 55P55, 55Q05, 55Q07, 55R05

27. CJM 1997 (vol 49 pp. 1089)

Burke, Maxim R.; Ciesielski, Krzysztof
Sets on which measurable functions are determined by their range
We study sets on which measurable real-valued functions on a measurable space with negligibles are determined by their range.

Keywords:measurable function, measurable space with negligibles, continuous image, set of range uniqueness (SRU)
Categories:28A20, 28A05, 54C05, 26A30, 03E35, 03E50
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