There is no exactly k-to-1 function from any continuum onto [0,1], or any dendrite, with only finitely many discontinuities. (English) Zbl 0649.54006

Heath, Jo. W.

Trans. Am. Math. Soc. 306, No. 1, 293-305 (1988).

Answering a question asked by H. Katsuura and K. Kellum [“k- to-1 functions on an arc”, Proc. Am. Math. Soc. 101, 629-633 (1987; Zbl 0632.54011)], the author shows that if an integer k is greater than 1, then each exactly k-to-1 function from a (compact, metric) continuum onto any dendrite (in particular, onto the closed unit interval of reals) must have infinitely many discontinuities.

Reviewer: J.J.Charatonik

MSC:

54C10	Special maps on topological spaces (open, closed, perfect, etc.)
54F50	Topological spaces of dimension \(\leq 1\); curves, dendrites
54C30	Real-valued functions in general topology

Keywords:

k-to-1 function; dendrite; closed unit interval; discontinuities

Citations:

Zbl 0632.54011