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On the Maćkowiak-Tymchatyn theorem. (English) Zbl 1072.54022
A continuum is a compact connected space, and a continuum is decomposable if it can be written as the union of two of its proper subcontinua. Otherwise we say it is indecomposable. If every subcontinuum of a continuum, $$X$$, is indecomposable then we say that $$X$$ is hereditarily indecomposable. A continuous mapping $$f:X\to Y$$ is called weakly confluent provided that every subcontinuum in the subcontinuum of $$Y$$ is an image of some subcontinuum of $$X$$. The Maćkowiak and Tymchatyn theorem states that every metric continuum is a weakly confluent image of some one-dimensional hereditarily indecomposable metric continuum. In the paper under review the authors utilize model-theoretic techniques to prove the Maćkowiak and Tymchatyn theorem. This is a quite interesting application of model theory to metric continuum theory.
##### MSC:
 54F15 Continua and generalizations 54C10 Special maps on topological spaces (open, closed, perfect, etc.) 06D05 Structure and representation theory of distributive lattices 03C98 Applications of model theory
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