Exponentiality for the construct of affine sets


  • Veerle Claes Vrije Universiteit Brussel




Topological construct, Affine space, Cartesian closed category, Cartesian closed topological hull, Exponential object


The topological construct SSET of affine sets over the two-point set S contains many interesting topological subconstructs such as TOP, the construct of topological spaces, and CL, the construct of closure spaces. For this category and its subconstructs cartesian closedness is studied. We first give a classification of the subconstructs of SSET according to their behaviour with respect to exponenttiality. We formulate sufficient conditions implying that a subconstruct behaves similar to CL. On the other hand, we characterize a conglomerate of subconstructs with behaviour similar to TOP. Finally, we construct the cartesian closed topological hull of SSET.


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Author Biography

Veerle Claes, Vrije Universiteit Brussel

WISK-IR, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium


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How to Cite

V. Claes, “Exponentiality for the construct of affine sets”, Appl. Gen. Topol., vol. 9, no. 1, pp. 21–32, Apr. 2008.



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