-to-
maps on hereditarily indecomposable continua
Author:
Jo Heath
Journal:
Trans. Amer. Math. Soc. 328 (1991), 433-444
MSC:
Primary 54C10; Secondary 54F15
DOI:
https://doi.org/10.1090/S0002-9947-1991-1028310-7
MathSciNet review:
1028310
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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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Additional Information
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