Geodesic
Exponentiability in lax slices of Top
Theory and applications of categories, Tome 16 (2006), pp. 218-235

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We consider exponentiable objects in lax slices of Top with respect to the specialization order (and its opposite) on a base space B. We begin by showing that the lax slice over B has binary products which are preserved by the forgetful functor to Top if and only if B is a meet (respective, join) semilattice in Top, and go on to characterize exponentiability over a complete Alexandrov space B.

Classification : 18B30, 18A40, 18A25, 54C35, 54F05, 06F30
Keywords: exponentiable space, function space, lax slice, specialization order 
Susan Niefield. Exponentiability in lax slices of Top. Theory and applications of categories, Tome 16 (2006), pp. 218-235. http://geodesic.mathdoc.fr/item/TAC_2006_16_a10/
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     author = {Susan Niefield},
     title = {Exponentiability in lax slices of {Top}},
     journal = {Theory and applications of categories},
     pages = {218--235},
     year = {2006},
     volume = {16},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2006_16_a10/}
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