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Exponentiable morphisms of domains

Published online by Cambridge University Press:  01 October 2008

F. CAGLIARI  and
S. MANTOVANI
F. CAGLIARI
Affiliation:
Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, I-40127 Bologna, Italy Email: [email protected]
S. MANTOVANI
Affiliation:
Dipartimento di Matematica, Università di Milano, Via Saldini 50, I-20133 Milano, Italy Email: [email protected]
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Abstract

Given a map f in the category ω-Cpo of ω-complete posets, exponentiability of f in ω-Cpo easily implies exponentiability of f in the category Pos of posets, while the converse is not true. We investigate the extra conditions needed on f exponentiable in Pos to be exponentiable in ω-Cpo by showing the existence of partial products of the two-point ordered set S={0<1} (Theorem 2.8). Using this characterisation and the embedding through the Scott topology of ω-Cpo in the category Top of topological spaces, we compare exponentiability in each setting and find that a morphism in ω-Cpo that is exponentiable in both Top and Pos is exponentiable in ω-Cpo also. Furthermore, we show that the exponentiability in Top and Pos are independent of each other.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 18 , Issue 5 , October 2008 , pp. 1005 - 1016
Copyright
Copyright © Cambridge University Press 2008

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