MONOTONE DECOMPOSITIONS OF INVERSE LIMIT SPACES BASED ON FINITE GRAPHS

A Θn,L graph is defined to be a compact, connected, locally connected metric space which is not separated into more than n components by any subcontinuum and no subcontinuum is separated into more than L components by any of its subcontinua. If X is a Θn,L graph and f is a continuous surjection of X onto X, then the inverse limit space (X,f) is a Θn continuum (not necessarily locally connected). Furthermore (X,f) admits a unique minimal monotone, upper semicontinuous decomposition D such that the quotient space (X,f)/D is a Θn,L graph if and only if (X,f) contains no indecomposable subcontinua with nonempty interior. © 1990.