Lightness of Induced Maps and Homeomorphisms

Abstract

Abstract. An example is given of a map f defined between arcwise connected continua such that C( f ) is light and 2 f is not light, giving a negative answer to a question of Charatonik and Charatonik. Furthermore, given a positive integer n, we study when the lightness of the induced map 2 f or Cn( f ) implies that f is a homeomorphism. Finally, we show a result in relation with the lightness of C(C( f )).