Definable one dimensional topologies in o-minimal structures

2018/07/21 by Peterzil, Ya'acov, Rosel, Ayala
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1807.08086

Abstract

We consider definable topological spaces of dimension one in o-minimal structures, and state several equivalent conditions for when such a topological space (X,τ) is definably homeomorphic to an affine definable space (namely, a definable subset of Mⁿ with the induced subspace topology). One of the main results says that it is sufficient for X to be regular and decompose into finitely many definably connected components.

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