Agradecimentos: This work was realized with the support of FAPESP (Fundação de Amparo a Pequisa do Estado de São Paulo) while a Visiting Professor at the "Universidade Estadual de Campinas" the second semester of 1992. I received generous logistic support from the "Centro de Logica Epistemologia e Historia da Ciencia" and the "Instituto de Matemática, Estatística e Ciência da Computação" of UNICAMP. Special thanks are due to A.M. Sette and C. Cifuentes for many stimulating ideas and discussions and their active participation in the seminary which originated this notes Ver menos

Abstract: We study [K, lambda] compactness of topological spaces in general and spaces of structures associated to abstract logics in particular. A characterization in terms of ultrafilter convergence of preservation of [k, lambda]-compactness by products of general topological spaces is given. The Abstract Compactness Theorem of Makowsky and Shelah becomes then a simple corollary from a general topological result. Reciprocally, several results on compactness shown first for logics are seen to hold true in all topological spaces Ver menos