Geodesic
A General Tychonoff Theorem for Multifunction
Canadian mathematical bulletin, Tome 17 (1974) no. 4, pp. 519-521

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Let {X a }a∈A be a non-empty family of compact spaces and let F be a subset of the m-product P{X a :a∈A}. The Tychonoff problem is the determination of the sets F which are pointwise compact. It is known that P{X a : a ∈ A} is pointwise compact [5, p. 400]. Also the set F of all point-closed multifunctions of P{X a :a∈ A) is pointwise compact. 
Fox, Geoffrey; Morales, Pedro. A General Tychonoff Theorem for Multifunction. Canadian mathematical bulletin, Tome 17 (1974) no. 4, pp. 519-521. doi: 10.4153/CMB-1974-091-8
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