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As indicated in the title, this paper was inspired by Smithson's work onArzel\`a-Ascoli theorem. Up to this point, the author's interest in the topichas led him to generalize Arzel\`a-Ascoli theorem in the context of uniformspaces. This approach was primarily influenced by J.L. Kelley's \textit{Generaltopology}. Soon after, the author learnt that in 1971, R.E. Smithson carriedover Kelley's approach to the case of point-compact multifunctions (rather thansingle-valued functions). Similarly, in this paper the author would like tocarry over the result, presented in his previous paper \textit{Arzel\`a-Ascolitheorem in uniform spaces}, to the case of point-compact multifunctions.

Short note on Smithson's paper concerning Arzel\`a-Ascoli theorem for multifunctions