Browsing by Author "Eleftheriou, P. E."
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- Definable group extensions in semi-bounded o-minimal structuresPublication . Edmundo, Mário; Eleftheriou, P. E.In this note we show: Let ℛ = 〈 R, <, +, 0,...〉 be a semi-bounded (respectively, linear) o-minimal expansion of an ordered group, and G a group definable in R of linear dimension m ([2]). Then G is a definable extension of a bounded (respectively, definably compact) definable group B by 〈 Rm, +〉.
- The universal covering homomorphism in o-minimal expansions of groupsPublication . Edmundo, Mário Jorge; Eleftheriou, P. E.Suppose G is a definably connected, definable group in an o-minimal expansion of an ordered group. We show that the o-minimal universal covering homomorphism p:U->G is a locally definable covering homomorphism and π_1(G) is isomorphic to the o-minimal fundamental group π (G) of G defined using locally definable covering homomorphisms.
- The universal covering map in o-minimal expansions of groupsPublication . Edmundo, Mário; Eleftheriou, P. E.; Prelli, L.In this paper we study locally definable manifolds and we prove: (i) the existence of universal locally definable covering maps; (ii) invariance results for locally definable covering maps, o-minimal fundamental groups and fundamental groupoids; (iii) monodromy equivalence for locally constant o-minimal sheaves; (iv) classification results for locally definable covering maps; (v) o-minimal Hurewicz and Seifert-van Kampen theorems.