Abstract
Many properties of continua, e.g., irreducibility, span zero, and various kinds of aposyndesis and unicoherence, are preserved by refinable maps or their inverses. The purpose of this paper is to consider the extent to which the property of being a θ n ′ {\theta ’_n} -continuum is preserved by refinable maps or by inverses of refinable maps. One consequence of this study is to generalize results of the first author where the domain or range is a graph. Several of his results are corollaries of ours.
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