Definable one dimensional topologies in o-minimal structures [article]

Ya'acov Peterzil, Ayala Rosel
2019 arXiv   pre-print
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 M^n 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.
arXiv:1807.08086v2 fatcat:cj6af5pk7zauhplz2y2cslcyju