It is a famous result of Alexandroff and Urysohn that every compact metric space is a continuous image of a Cantor set ∆. In this short note we complement this result by showing that a certain uniqueness property holds. Namely, if (K,d) is a compact metric space and f and g are two continuous mappings from ∆ onto K, the, for every e > 0 there exists a homeomorphism phi of ∆ such that d(g(x), f(phi(x))) < e for all x∆.
@article{urn:eudml:doc:38749,
title = {On continuous surjections from Cantor set.},
journal = {Extracta Mathematicae},
volume = {19},
year = {2004},
pages = {335-337},
zbl = {1064.54033},
mrnumber = {MR2135830},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38749}
}
Cabello Sánchez, Félix. On continuous surjections from Cantor set.. Extracta Mathematicae, Tome 19 (2004) pp. 335-337. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38749/