Geodesic
On approximate inverse systems and resolutions
Fundamenta Mathematicae, Tome 142 (1993) no. 3, pp. 241-255.

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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 $p_{aa'}$ are not subject to the commutativity requirement $p_{aa' p_{a'a''} = p_{aa''}, a ≤ a' ≤ a''$. Instead, the mappings $p_{aa'}p_{a'a''}$ and $p_{aa''}$ are allowed to differ in a way controlled by coverings $U_a$, called meshes, which are associated with the members $X_a$ 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.
DOI : 10.4064/fm-142-3-241-255
Keywords: inverse system, approximate inverse system, inverse limit, resolution, approximate resolution, dimension

Sibe Mardešić 1

1 
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Sibe Mardešić. On approximate inverse systems and resolutions. Fundamenta Mathematicae, Tome 142 (1993) no. 3, pp. 241-255. doi : 10.4064/fm-142-3-241-255. http://geodesic.mathdoc.fr/articles/10.4064/fm-142-3-241-255/

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