Fernando Galván, José Francisco2024-01-232024-01-23201810.1016/j.aim.2018.04.011https://hdl.handle.net/20.500.14352/94908In this work we characterize the subsets of Rn that are images of Nash maps f : Rm → Rn. We prove Shiota’s conjecture and show that a subset S ⊂ Rn is the image of a Nash map f : Rm → Rn if and only if S is semialgebraic, pure dimensional of dimension d ≤ m and there exists an analytic path α : [0, 1] → S whose image meets all the connected components of the set of regular points of S. Two remarkable consequences are the following: (1) pure dimensional irreducible semialgebraic sets of dimension d with arc-symmetric closure are Nash images of Rd; and (2) semialgebraic sets are projections of irreducible algebraic sets whose connected components are Nash diffeomorphic to Euclidean spaces.engjournal articlehttps://doi.org/10.1016/j.aim.2018.04.011https://www.sciencedirect.com/science/article/pii/S0001870818301518restricted accessNash imageArc-symmetric semialgebraic setDesingularizationDrilling blow-upWell-welded semialgebraic setNash path-connected semialgebraic setCiencias12 Matemáticas