Openness of the induced map cn(f)
Given a map between compact metric spaces f : X-- and gt;Y , it is possible to induce a map between the n-fold hyperspaces Cn(f) : Cn(X) -- and gt; Cn(Y ) for each positive integer n. Let A and B be classes of maps. A general problem is to find the interrelations between the following two statements...
- Autores:
-
Camargo, Javier
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2009
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/73768
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/73768
http://bdigital.unal.edu.co/38245/
- Palabra clave:
- continua
hyperspaces of continua
induced maps
open maps.
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | Given a map between compact metric spaces f : X-- and gt;Y , it is possible to induce a map between the n-fold hyperspaces Cn(f) : Cn(X) -- and gt; Cn(Y ) for each positive integer n. Let A and B be classes of maps. A general problem is to find the interrelations between the following two statements:1. f 2 A; 2. Cn(f) 2 B. It is known that 1 and 2 are equivalentconditions if both A and B are the class of homeomorphisms. If A and B are the class of open maps, then the openness of Cn(f) implies the openness of f. Furthermore, there exists an open map f such that Cn(f) is not open. Moreover, if Cn(f) is open and n and gt; 3, then f is both open and monotone. Our main result is Theorem 3.2, where we prove that if the induced map Cn(f) is an open map, for n and gt;= 2, then f is a homeomorphism. |
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