On approximate inverse systems and resolutions
نویسنده
چکیده
Recently, L. R. Rubin, T. Watanabe and the author have introduced approximate inverse systems and approximate resolutions, a new tool designed to study topological spaces. These systems differ from the usual inverse systems in that the bonding maps paa′ are not subject to the commutativity requirement paa′pa′a′′ = paa′′ , a ≤ a′ ≤ a′′. Instead, the mappings paa′pa′a′′ and paa′′ are allowed to differ in a way controlled by coverings Ua, called meshes, which are associated with the members Xa of the system. The purpose of this paper is to consider a more general and much simpler notion of approximate system and approximate resolution, which does not require meshes. The main result is a construction which associates with any approximate resolution in the new sense an approximate resolution in the previous sense in such a way that previously obtained results remain valid in the present more general setting.
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