an:02076195
Zbl 1072.54022
Hart, Klaas Pieter; van der Steeg, B. J.
On the Ma??kowiak-Tymchatyn theorem
EN
Acta Univ. Carol., Math. Phys. 43, No. 2, 27-43 (2002).
00091397
2002
j
54F15 54C10 06D05 03C98
metric continuum; weakly confluent; indecomposable metric continuum; model theory
A \textit{continuum} is a compact connected space, and a continuum is \textit{decomposable} if it can be written as the union of two of its proper subcontinua. Otherwise we say it is \textit{indecomposable}. If every subcontinuum of a continuum, \(X\), is indecomposable then we say that \(X\) is \textit{hereditarily indecomposable}. A continuous mapping \(f:X\to Y\) is called \textit{weakly confluent} provided that every subcontinuum in the subcontinuum of \(Y\) is an image of some subcontinuum of \(X\). The Ma??kowiak 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 Ma??kowiak and Tymchatyn theorem. This is a quite interesting application of model theory to metric continuum theory.
Brian Raines (Waco)