Beer, GeraldGarrido Carballo, María IsabelAmigó, J.M.Cánovas, M.J.López-Cerdá, M.A.López-Pellicer, M.2025-12-122025-12-122023Beer, G., Isabel Garrido, M. Reciprocation and Pointwise Product in Vector Lattices of Functions. In: Amigó, J.M., Cánovas, M.J., López-Cerdá, M.A., López-Pellicer, M. (eds) Functional Analysis and Continuous Optimization. IMFACO 2022. Springer Proceedings in Mathematics & Statistics.2023 02 Jul; vol 424978303130013497830313001412194-10092194-101710.1007/978-3-031-30014-1_3https://hdl.handle.net/20.500.14352/128843Dedicated to Juan Carlos Ferrando on the occasion of his 65th birthdayIf [omega] is a vector lattice of real-valued functions defined on a set containing the constant functions such that the reciprocal of each nonvanishing member of [omega] remains in [omega] , then [omega] is stable under pointwise product. We survey the literature on stability under reciprocation and pointwise product in the context of metric domains, with particular attention given to the uniformly continuous real-valued functions defined on them. For the first time, we present necessary and sufficient conditions for stability for the vector lattice of real-valued coarse maps defined on an arbitrary metric space. Membership of a function to this class means that its associated modulus of continuity is finite-valued, and need not entail continuity of the function.engbook partmetadata only accessTopologíaAnálisis funcional y teoría de operadores1210 Topología1202 Análisis y Análisis Funcional