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In this note, we prove that all compact Hausdorff topological spaces are exponential objects in the category UAP of uniform approach spaces and contractions as introduced in R. Lowen, Approach Spaces: the Missing Link in the Topology-Uniformity-Metric Triad, Oxford University Press, 1997. As a consequence, we show that UAP admits at least as many monoidal closed structures as there are infinite cardinals. We also prove that under the assumption that no measurable cardinals exist, there exists a proper conglomerate of these monoidal closed structures on UAP. [Copyright &y& Elsevier]