Tree-like continua and exactly 𝑘-to-1 functions

Author:

Heath Jo

Abstract

To answer a question of Nadler and Ward, k k -to- 1 1 maps from tree-like continua onto tree-like continua are constructed, for k > 2 k > 2 . It is shown that certain arc-like continua cannot be the domain of any 2 2 -to- 1 1 map and that certain tree-like continua cannot be the image of any 2 2 -to- 1 1 map (defined on continua) but it is unknown if any indecomposable arc-like continuum can be the domain or any tree-like continuum the image of a 2 2 -to- 1 1 map.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference11 articles.

1. D. Fox, 𝑘-to-1 continuous transformations, University of California at Riverside Dissertation, August 1973.

2. On 𝑘-to-1 transformations;Gottschalk, W. H.;Bull. Amer. Math. Soc.,1947

3. The non-existence of a certain type of continuous transformation;Harrold, O. G., Jr.;Duke Math. J.,1939

4. There is no exactly 𝑘-to-1 function from any continuum onto [0,1], or any dendrite, with only finitely many discontinuities;Heath, Jo W.;Trans. Amer. Math. Soc.,1988

5. Every exactly 2-to-1 function on the reals has an infinite set of discontinuities;Heath, Jo;Proc. Amer. Math. Soc.,1986

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