Geodesic
Exponentiability of perfect maps: four approaches
Theory and applications of categories, Tome 10 (2002), pp. 127-133
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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.

Classification : 54C35, 54C10, 18B30, 18D15.
Keywords: exponentiable, perfect, proper, separated, function space. 
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     author = {Susan Niefield},
     title = {Exponentiability of perfect maps: four approaches},
     journal = {Theory and applications of categories},
     pages = {127--133},
     year = {2002},
     volume = {10},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2002_10_a4/}
}
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Susan Niefield. Exponentiability of perfect maps: four approaches. Theory and applications of categories, Tome 10 (2002), pp. 127-133. http://geodesic.mathdoc.fr/item/TAC_2002_10_a4/