Publicado
2009-07-01
Openness of the induced map Cn(f)
Palabras clave:
continua, hyperspaces of continua, induced maps, open maps. (es)Descargas
Given a map between compact metric spaces f : X-->Y , it is possible to induce a map between the n-fold hyperspaces Cn(f) : Cn(X) --> 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 equivalent
conditions 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 > 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 >= 2, then f is a homeomorphism.
Cómo citar
APA
Camargo, J. (2009). Openness of the induced map Cn(f). Boletín de Matemáticas, 16(2), 115–123. https://revistas.unal.edu.co/index.php/bolma/article/view/40781
ACM
[1]
Camargo, J. 2009. Openness of the induced map Cn(f). Boletín de Matemáticas. 16, 2 (jul. 2009), 115–123.
ACS
(1)
Camargo, J. Openness of the induced map Cn(f). Bol. Mat. 2009, 16, 115-123.
ABNT
CAMARGO, J. Openness of the induced map Cn(f). Boletín de Matemáticas, [S. l.], v. 16, n. 2, p. 115–123, 2009. Disponível em: https://revistas.unal.edu.co/index.php/bolma/article/view/40781. Acesso em: 24 abr. 2024.
Chicago
Camargo, Javier. 2009. «Openness of the induced map Cn(f)». Boletín De Matemáticas 16 (2):115-23. https://revistas.unal.edu.co/index.php/bolma/article/view/40781.
Harvard
Camargo, J. (2009) «Openness of the induced map Cn(f)», Boletín de Matemáticas, 16(2), pp. 115–123. Disponible en: https://revistas.unal.edu.co/index.php/bolma/article/view/40781 (Accedido: 24 abril 2024).
IEEE
[1]
J. Camargo, «Openness of the induced map Cn(f)», Bol. Mat., vol. 16, n.º 2, pp. 115–123, jul. 2009.
MLA
Camargo, J. «Openness of the induced map Cn(f)». Boletín de Matemáticas, vol. 16, n.º 2, julio de 2009, pp. 115-23, https://revistas.unal.edu.co/index.php/bolma/article/view/40781.
Turabian
Camargo, Javier. «Openness of the induced map Cn(f)». Boletín de Matemáticas 16, no. 2 (julio 1, 2009): 115–123. Accedido abril 24, 2024. https://revistas.unal.edu.co/index.php/bolma/article/view/40781.
Vancouver
1.
Camargo J. Openness of the induced map Cn(f). Bol. Mat. [Internet]. 1 de julio de 2009 [citado 24 de abril de 2024];16(2):115-23. Disponible en: https://revistas.unal.edu.co/index.php/bolma/article/view/40781
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Derechos de autor 2009 Boletín de Matemáticas
Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.