Buckethandle

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A buckethandle continuum is a Knaster continuum where $f_n(t)=1-|2t-1|$. The double buckethandle is a Knaster continuum defined as an inverse limit with the bonding maps $$f_n(x) = \left\{ \begin{array}{ll} 3t & 0 \leq t \leq \dfrac{1}{3} \\ 2-3t & \dfrac{1}{3} \leq t \leq \dfrac{2}{3} \\ 3t-2 & \dfrac{2}{3} \leq t \leq 1. \end{array} \right.$$

Buckethandle.png

Properties

Theorem: The buckethandle continuum is indecomposable.

Proof: