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Definable compactness in o-minimal structures (2405.07112v2)
Published 12 May 2024 in math.LO and math.GN
Abstract: We characterize the notion of definable compactness for topological spaces definable in o-minimal structures, answering questions of Peterzil and Steinhorn (1999) and Johnson (2018). Specifically, we prove the equivalence of various definitions of definable compactness in the literature, including those in terms of definable curves, definable types, and definable downward directed families of closed sets.