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20212023
most citedOne-dimensional definable topological spaces in o-minimal structures

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math.LO2023★ 1 cited

One-dimensional definable topological spaces in o-minimal structures

Pablo Andújar Guerrero, Margaret E. M. Thomas

We study the properties of topological spaces , where is a definable set in an o-minimal structure and the topology on has a basis that is (uniformly) definable.…

math.LO2023

The Marker-Steinhorn Theorem

Pablo Andújar Guerrero

We give a proof of the Marker-Steinhorn Theorem which fills a gap in previous proofs of the result.

math.LO2023

Cardinality of definable families of sets in o-minimal structures

Pablo Andújar Guerrero

We prove that any definable family of subsets of a definable infinite set in an o-minimal structure has cardinality at most . We derive some consequences in terms of count…