Induced almost continuous functions on hyperspaces

• Autorzy: Alejandro Illanes
• Języki publikacji: EN

Abstrakty

EN

For a metric continuum X, let C(X) (resp., $2^{X}$) be the hyperspace of subcontinua (resp., nonempty closed subsets) of X. Let f: X → Y be an almost continuous function. Let C(f): C(X) → C(Y) and $2^{f}: 2^{X} → 2^{Y}$ be the induced functions given by $C(f)(A) = cl_{Y}(f(A))$ and $2^{f}(A) = cl_{Y}(f(A))$. In this paper, we prove that:
• If $2^{f}$ is almost continuous, then f is continuous.
• If C(f) is almost continuous and X is locally connected, then f is continuous.
• If X is not locally connected, then there exists an almost continuous function f: X → [0,1] such that C(f) is almost continuous and f is not continuous.

Kategorie tematyczne

• 54B20: Hyperspaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2006
• Tom: 105
• Numer: 1
• Strony: 69-76

Daty

wydano

2006

Twórcy

autor

Alejandro Illanes

• Instituto de Matematicas, UNAM, Circuito Exterior, Ciudad Universitaria, 04510 México, D.F., Mexico

Identyfikatory

DOI

10.4064/cm105-1-8