Abstract
Recently, S. Mardešić and L.R. Rubin have defined approximate inverse systems of compacta. In these systems the bonding maps commute only up to certain controlled values. In this paper it is shown that such systems are stable in the sense that small perturbations of bonding maps yield again an approximate system and do not affect the limit space. In particular, an inverse system of near homeomorphisms can be replaced by an approximate inverse system of homeomorphisms having the same limit space. In such a system projections from the limit space need not be (near) homeomorphisms, but are always refinable maps.
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