Geodesic
Cartesian closed topological hull of the construct of closure spaces
Theory and applications of categories, Tome 8 (2001), pp. 481-489

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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.

Classification : 54A05, 18D15, 54C35.
Keywords: closure space, cartesian closedness, function space, cartesian closed topological hull. 
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     author = {V. Claes and E. Lowen-Colebunders and G. Sonck},
     title = {Cartesian closed topological hull of the construct of closure spaces},
     journal = {Theory and applications of categories},
     pages = {481--489},
     publisher = {mathdoc},
     volume = {8},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2001_8_a17/}
}
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V. Claes; E. Lowen-Colebunders; G. Sonck. Cartesian closed topological hull of the construct of closure spaces. Theory and applications of categories, Tome 8 (2001), pp. 481-489. http://geodesic.mathdoc.fr/item/TAC_2001_8_a17/