engleski

There are no essential phantom mappings from 1-dimensional CW-complexes

A phantom mapping h from a space Z to a space Y is a mapping whose restrictions to compact subsets are homotopic to constant mappings. If the mapping is not homotopic to a constant mapping, one speaks of an essential phantom mapping. In a previous paper the author showed that there are no essential phantom mappings between CW-complexes, if dimension of Y  does not exceed 1. In the present paper it is shown that there are no essential phantom mappings between CW-complexes if dimension of Z  does not exceed 1. There exist an essential phantom mapping from Z to Y, where dim Z = dim Y = 1, Y is a CW-complex, but Z is not.

homotopy classification of mappings ; phantom mappings ; 1-dimensional CW-complexes

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