There Are No Essential Phantom Mappings from 1-dimensional CW-complexes

Sibe Mardešić. "There Are No Essential Phantom Mappings from 1-dimensional CW-complexes." Bulletin of the Polish Academy of Sciences. Mathematics 61.2 (2013): 141-147. <http://eudml.org/doc/281189>.

@article{SibeMardešić2013,
abstract = {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 dim Y ≤ 1. In the present paper it is shown that there are no essential phantom mappings between CW-complexes if dim Z ≤ 1. In contrast, there exist essential phantom pairs of mappings between CW-complexes where dim Z = 1 and dim Y = 2. Moreover, there exist essential phantom mappings with dim Z = dim Y = 1 where Y is a CW-complex, but Z is not.},
author = {Sibe Mardešić},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {homotopy classification of mappings; phantom mappings; 1-dimensional CW-complexes},
language = {eng},
number = {2},
pages = {141-147},
title = {There Are No Essential Phantom Mappings from 1-dimensional CW-complexes},
url = {http://eudml.org/doc/281189},
volume = {61},
year = {2013},
}

TY - JOUR
AU - Sibe Mardešić
TI - There Are No Essential Phantom Mappings from 1-dimensional CW-complexes
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2013
VL - 61
IS - 2
SP - 141
EP - 147
AB - 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 dim Y ≤ 1. In the present paper it is shown that there are no essential phantom mappings between CW-complexes if dim Z ≤ 1. In contrast, there exist essential phantom pairs of mappings between CW-complexes where dim Z = 1 and dim Y = 2. Moreover, there exist essential phantom mappings with dim Z = dim Y = 1 where Y is a CW-complex, but Z is not.
LA - eng
KW - homotopy classification of mappings; phantom mappings; 1-dimensional CW-complexes
UR - http://eudml.org/doc/281189
ER -