Abstract
It is well known that there exist separable, metrizable, totally disconnected spaces of all dimensions. In this note we introduce the notion of an almost 0-dimensional space and prove that every such space is a totally disconnected subspace of an R-tree and, hence, at most 1-dimensional. As applications we prove that the spaces of homeomorphisms of the universal Menger continua are 1-dimensional and that hereditarily locally connected spaces have dimension at most two.
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