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Content available remote There Are No Essential Phantom Mappings from 1-dimensional CW-complexes
Mardešić S.
Bulletin of the Polish Academy of Sciences. Mathematics
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2013
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Vol. 61, no 2
141--147
EN
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 h is not homotopic to a constant mapping, one speaks of an essential phantom mapping. The definition of (essential) phantom pairs of mappings is analogous. In the study of phantom mappings (phantom pairs of mappings), of primary interest is the case when Z and Y are CW-complexes. In a previous paper it was shown that there are no essential phantom mappings (pairs of phantom mappings) between CW-complexes if dimY≤1. In the present paper it is shown that there are no essential phantom mappings between CW-complexes if dimZ≤1. In contrast, there exist essential phantom pairs of mappings between CW-complexes where dimZ=1 and dimY=2. Moreover, there exist essential phantom mappings with dimZ=dimY=1 where Y is a CW-complex, but Z is not.
2
Content available remote There are no phantom pairs of mappings to 1-dimensional CW-complexes
Mardešić S.
Bulletin of the Polish Academy of Sciences. Mathematics
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2007
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Vol. 55, no 4
365-371
EN
Two mappings from a CW-complex to a 1-dimensional CW-complex are homotopic if and only if their restrictions to finite subcomplexes are homotopic.
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