Exponentiality for the construct of affine sets

Claes, Veerle ^[1]
1. [1] Vrije Universiteit Brussel
  
  Vrije Universiteit Brussel
  
  Arrondissement Brussel-Hoofdstad, Bélgica
Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 9, Nº. 1, 2008, págs. 21-32
Idioma: inglés
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Resumen
- 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.