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arXiv · 2604.12517

The converse to Borsuk's result on fans fails

Benjamin Vejnar
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Abstract

A fan is an arc-wise connected hereditarily unicoherent continuum with exactly one branching point. By a result of Borsuk, every fan is a 1-dimensional continuum that can be expressed as the union of a family of arcs, each pair of which intersects in the branching point. In this paper, we prove that the converse does not hold by providing a more general result.

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Benjamin Vejnar. 2026-04-14. The converse to Borsuk's result on fans fails. https://arxiv.org/abs/2604.12517

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