Two proofs of the exponentiability of perfect maps are presented and compared to two other recent approaches. One of the proofs is an elementaryapproach including a direct construction of the exponentials. The other, implicit in the literature, uses internal locales in the topos of set-valued sheaves on a topological space.
Keywords: exponentiable, perfect, proper, separated, function space.
2000 MSC: 54C35, 54C10, 18B30, 18D15.
Theory and Applications of Categories, Vol. 10, 2002, No. 5, pp 127-133.
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