engleski

Stability of gauged approximate resolutions

This paper deals with the stability of (gauged) resolutions, i.e. with the property that small perturbations of bonding maps of an approximate resolution yield again an approximate resolution of the same space. A sufficient condition for stability is found, which depends only on the cardinality of the indexing set. It is shown that small perturbations do not affect the isomorphism class of an approximate resolution. Moreover, every approximate resolution is isomorphic to an approximate resolution which satisfies the stability condition. In that way the analogous results of S.Mardešić and J.Segal (which concern approximate resolutions of metric compacta) are generalized to approximate resolutions consisting of topologically complete spaces.

gauged systems; resolutions; approximate resolutions; topologicallycomplete spaces

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