Cartesian closed topological hull of the construct of closure spaces

V. Claes, E. Lowen-Colebunders and G. Sonck

A cartesian closed topological hull of the construct CLS of closure spaces and continuous maps is constructed. The construction is performed in two steps. First a cartesian closed extension L of CLS is obtained. We apply a method worked out by J. Adamek and J. Reiterman for constructing extensions of constructs that in some sense ``resemble'' the construct of uniform spaces. Secondly, within this extension L the cartesian closed topological hull L* of CLS is characterized as a full subconstruct. In order to find the internal characterization of the objects of L* we produce a concrete functor to the category of power closed collections based on CLS as introduced by J. Adamek, J. Reiterman and G.E. Strecker.

Keywords: closure space, cartesian closedness, function space, cartesian closed topological hull.

2000 MSC: 54A05, 18D15, 54C35.

Theory and Applications of Categories, Vol. 8, 2001, No. 18, pp 481-489.

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