On Minc's sheltered middle path
Du\v{s}an Repov\v{s}, Witold Rosicki, \v{Z}iga Virk, Andreas, Zastrow
TL;DR
This paper examines Minc's sheltered middle path construction and demonstrates that, in the case of general paths, it can produce the topologist's sine curve, highlighting limitations in non-PL contexts.
Contribution
It reveals that Minc's construction, when applied to non-PL paths, can lead to the topologist's sine curve, showing a significant limitation in the method.
Findings
Minc's sheltered middle path can produce the topologist's sine curve for non-PL paths.
The construction's behavior differs significantly between PL and non-PL paths.
The result impacts the understanding of path transformations in topology.
Abstract
This paper shows that a construction, which was introduced by Piotr Minc in connection with a problem that came from Helly type theorems and that allows to replace three PL-arcs with a "sheltered middle path", can in the case of general (non-PL) paths result in the topologist's sine curve.
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