-to- maps on hereditarily indecomposable continua

Author:
Jo Heath

Journal:
Trans. Amer. Math. Soc. **328** (1991), 433-444

MSC:
Primary 54C10; Secondary 54F15

MathSciNet review:
1028310

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Abstract: Suppose is a continuous map from the hereditarily indecomposable continuum onto a continuum . In order for it to be the case that each proper subcontinuum in has as its preimage two disjoint continua each of which maps homeomorphically onto , it is obviously necessary that satisfy the condition that each nondense connected subset of has disconnected preimage. We show that this condition is also sufficient, and thus any continuous map from a hereditarily indecomposable continuum satisfying this condition must be confluent and have an image that is hereditarily indecomposable.

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DOI:
https://doi.org/10.1090/S0002-9947-1991-1028310-7

Keywords:
Hereditarily indecomposable continua,
function,
map,
map,
function

Article copyright:
© Copyright 1991
American Mathematical Society