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Hyperspaces and open monotone maps of hereditarily indecomposable continua |
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| Authors: | Michael Levin |
| Affiliation: | Department of Mathematics, Haifa University, Mount Carmel, Haifa 31905, Israel |
| Abstract: | We prove the following theorems: Theorem 1. Let Theorem 2. For every open monotone map The connection between these theorems and other results in Hyperspace theory is studied. |
| Keywords: | Hyperspaces hereditarily indecomposable continua open monotone maps |
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be an 
-dimensional hereditarily indecomposable continuum. Then there exist 
-dimensional hereditarily indecomposable continua 
and monotone maps 
such that 
is an embedding and the space 
of all subcontinua of 
is embeddable in 
by 
. 
with non-trivial sufficiently small fibers on a finite dimensional hereditarily indecomposable continuum 
with 
there exists a 
-dimensional subcontinuum 
such that 
and the restriction of 
to 
is also monotone and open.