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.
Keywords: exponentiable space, function space, lax slice, specialization order
2000 MSC: 18B30, 18A40, 18A25, 54C35, 54F05, 06F30
Theory and Applications of Categories,
Vol. 16, 2006,
No. 11, pp 218-235.
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