# On continuous surjections from Cantor set.

Extracta Mathematicae (2004)

- Volume: 19, Issue: 3, page 335-337
- ISSN: 0213-8743

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topCabello Sánchez, Félix. "On continuous surjections from Cantor set.." Extracta Mathematicae 19.3 (2004): 335-337. <http://eudml.org/doc/38749>.

@article{CabelloSánchez2004,

abstract = {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∆.},

author = {Cabello Sánchez, Félix},

journal = {Extracta Mathematicae},

keywords = {Espacios topológicos; Aplicaciones continuas; Sobreyectividad; Conjuntos de Cantor},

language = {eng},

number = {3},

pages = {335-337},

title = {On continuous surjections from Cantor set.},

url = {http://eudml.org/doc/38749},

volume = {19},

year = {2004},

}

TY - JOUR

AU - Cabello Sánchez, Félix

TI - On continuous surjections from Cantor set.

JO - Extracta Mathematicae

PY - 2004

VL - 19

IS - 3

SP - 335

EP - 337

AB - 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∆.

LA - eng

KW - Espacios topológicos; Aplicaciones continuas; Sobreyectividad; Conjuntos de Cantor

UR - http://eudml.org/doc/38749

ER -