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In this paper, we first characterize those compatible metrics d on a metrizable space X which give rise to a connected dproximal hyperspace. We show that the space of irrational numbers, in particular, admits a complete metric with this property and, as a consequence, we get a negative answer to a question of [11] about selections for hyperspace topologies. Next, we characterize the compatible metrics on X which are uniformly equivalent to ultrametrics showing that this is equivalent to the zero-dimensionality of the corresponding proximal hyperspaces. Applications and related results about other disconnectedness-like properties of proximal hyperspaces are obtained.

Recognizing special metrics by topological properties of the ``metri''-proximal hyperspace