Geodesic
There Are No Essential Phantom Mappings from $1$-dimensional CW-complexes
Sibe Mardešić1
1 Department of Mathematics University of Zagreb Bijenička cesta 30 10 002 Zagreb, P.O. Box 335, Croatia
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 61 (2013) no. 2, pp. 141-147.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $\mathop{\rm dim}Y\leq 1$. In the present paper it is shown that there are no essential phantom mappings between CW-complexes if $\mathop{\rm dim}Z\leq 1$. In contrast, there exist essential phantom pairs of mappings between CW-complexes where $\mathop{\rm dim}Z=1$ and $\mathop{\rm dim}Y=2$. Moreover, there exist essential phantom mappings with $\mathop{\rm dim}Z=\mathop{\rm dim}Y=1$ where $Y$ is a CW-complex, but $Z$ is not.
DOI : 10.4064/ba61-2-7
Keywords: phantom mapping space space mapping whose restrictions compact subsets homotopic constant mappings mapping homotopic constant mapping speaks essential phantom mapping definition essential phantom pairs mappings analogous study phantom mappings phantom pairs mappings primary interest cw complexes previous paper shown there essential phantom mappings pairs phantom mappings between cw complexes mathop dim leq present paper shown there essential phantom mappings between cw complexes mathop dim leq contrast there exist essential phantom pairs mappings between cw complexes where mathop dim mathop dim moreover there exist essential phantom mappings mathop dim mathop dim where cw complex

Sibe Mardešić 1

1 Department of Mathematics University of Zagreb Bijenička cesta 30 10 002 Zagreb, P.O. Box 335, Croatia 
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Sibe Mardešić. There Are No Essential Phantom Mappings
 from $1$-dimensional CW-complexes. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 61 (2013) no. 2, pp. 141-147. doi : 10.4064/ba61-2-7. http://geodesic.mathdoc.fr/articles/10.4064/ba61-2-7/

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