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.
Theory and Applications of Categories, Vol. 8, 2001, No. 18, pp 481-489. http://www.tac.mta.ca/tac/volumes/8/n18/n18.dvi http://www.tac.mta.ca/tac/volumes/8/n18/n18.ps http://www.tac.mta.ca/tac/volumes/8/n18/n18.pdf ftp://ftp.tac.mta.ca/pub/tac/html/volumes/8/n18/n18.dvi ftp://ftp.tac.mta.ca/pub/tac/html/volumes/8/n18/n18.psTAC Home