Universidad Complutense de Madrid
E-Prints Complutense

On divisibility in shape theory.

Impacto

Downloads

Downloads per month over past year



Laguna, V. F. and Rodríguez Sanjurjo, José Manuel (1994) On divisibility in shape theory. In Contribuciones matemáticas: Libro-homenaje al Profesor D. José Javier Etayo Miqueo. Editorial Complutense, Madrid, pp. 239-243. ISBN 84-7491-510-4



Abstract

Given two shape morphisms F,G:X→Y , where X and Y are compacta, one declares F to be a divisor of G provided for any compactum Z and any shape morphism U:X→Z if F factors as F=F 1 ∘U , then G factors as G=G 1 ∘U . On the other hand, if Sh(X,Y) is a group, then F being a divisor of G ought to mean that G=mF for some integer m . In particular, if Y=S n is the n -sphere, then Sh(X,S n )=[X,S n ] can be given the structure of a group (the n th cohomotopy group) if the shape dimension of X is at most 2n−1 . Here is the main result of the paper.
Theorem. If F,G:X→S n and the shape dimension of X is at most n , then F is the divisor of G iff G=mF for some integer m in the n th cohomotopy group of X.


Item Type:Book Section
Uncontrolled Keywords:divisibility in shape theory; divisibility of mappings
Subjects:Sciences > Mathematics > Topology
ID Code:21886
Deposited On:18 Jun 2013 06:57
Last Modified:12 Dec 2018 15:13

Origin of downloads

Repository Staff Only: item control page