Exponentiability in Stone spaces and Priestley spaces

Author: Evgeny Kuznetsovi
Keywords: Stone space, Priestley space, Exponentiability
Annotation:

Exponentiability problem is studied for Stone topological spaces and Priestley partially ordered topological spaces. In setting of Stone spaces is shown that exponentiable objects are exactly the spaces with nite underlying set; ex- ponentiable morphisms are exactly local homeomorphisms. In setting of Priestley spaces is shown that exponentiable objects are exactly the spaces with nite underlying set; exponentiability of morphisms is investigated partially, in particular a necessary condition is found and necessary and sufficient condition is proved for a projections from a product over base.