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Published online by Cambridge University Press: 09 April 2009
In this paper we show that a locally connected and locally compact metric image of a generalized graph under a reflexive open mapping is a generalized graph; further, we characterize all acyclic generalized graphs X with the property that any locally one-to-one reflexive open mapping of X into a Hausdorff space is globally one-to-one. Several problems are posed and some examples are given.