Abstract
Abstract
The Reeb graph is instrumental in extracting topological features from contour plots. In this context, the Reeb ordering method offers both a natural discretisation and an algorithmic approach to compute a Reeb tree. Our main theorem establishes stability within the interleaving distance among order-compatible topological spaces. Our contributions are fourfold: we construct the reflector functor for quotient structures in ordered spaces, introduce generalised trees in poset terms, define branch completeness for graph-like posets, and prove a strong normalisation theorem for posets. Furthermore, our interleaving distance metric makes our stability estimate much finer than the preceding study.
Publisher
Research Square Platform LLC
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