Abstract:
We study a Möbius-invariant generalization, called BTR, of the classical property of bounded turning in a metric space which was introduced by Tukia and Väisälä in 1980 and suitable for use in Ptolemaic Möbius structures in the sense of Buyalo. In particular, we prove that every continuum with the BTR property, lying on the boundary of a domain in the complex plane, is locally connected.
Keywords:Möbius structure, Ptolemaic Möbius space, continuum with bounded turning, quasimöbius arc, quasimöbiusly connected space, local connectedness.
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