Garrido Carballo, María IsabelJaramillo Aguado, Jesús Ángel2023-06-202023-06-202004Garrido, M. I., y J. A. Jaramillo. «Homomorphisms on Function Lattices». Monatshefte for Mathematik, vol. 141, n.o 2, febrero de 2004, pp. 127-46. DOI.org (Crossref), https://doi.org/10.1007/s00605-002-0011-4.0026-925510.1007/s00605-002-0011-4https://hdl.handle.net/20.500.14352/49985This paper was carried out while the first author was a visitor at the Universidad Complutense de Madrid. It is a pleasure to thank the Departamento de Ana´lisis Matema´tico of this University for its hospitality. Thanks are also due to Professors Javier Gomez, Manuel Alonso Moron and Angeles Prieto for several helpful conversations concerning this paper.In this paper we study real lattice homomorphisms on a unital vector lattice L subset of C(X), where X is a completely regular space. We stress on topological properties of its structure spaces and on its representation as point evaluations. These results are applied to the lattice L = Lip(X) of real Lipschitz functions on a metric space. Using the automatic continuity of lattice homomorphisms with respect to the Lipschitz norm, we are able to derive a Banach-Stone theorem in this context. Namely, it is proved that the unital vector lattice structure of Lip (X) characterizes the Lipschitz structure of the complete metric space X. In the case L = Lip (X) of bounded Lipschitz functions, an analogous result is obtained in the class of complete quasiconvex metric spaces.engjournal articlehttps://doi.org/10.1007/s00605-002-0011-4http://www.springerlink.comrestricted access517.98515.1Lattices of continuous functionslattice homomorphismsLipschitz functionsBanach-Stone-theoremsAnálisis funcional y teoría de operadoresTopología1210 Topología