A simple construction of meshes in approximate systems

Abstract

Recently, S. Mardešič, L. R. Rubin and T. Watanabe have developed a theory of approximate inverse systems and approximate resolutions, providing thus a new tool to study topological spaces. M. G. Charalambous then introduced a somewhat simpler but more general notion of approximate system. Subsequently, S. Mardešič showed, by a rather general and complicated construction, that the two notions of approximate systems (approximate resolutions) share all relevant properties of their limits (resolutions). This paper presents a new and rather simple construction with the same properties. Moreover, in the case of topologically complete approximate resolutions, uniqueness up to isomorphisms is established. At the end, it is indicated how one can extend this construction onto approximate mappings.