The quasitopos hull of the construct of closure spaces

Authors

  • Veerle Claes Vrije Universiteit Brussel
  • G. Sonck Vrije Universiteit Brussel

DOI:

https://doi.org/10.4995/agt.2003.2006

Keywords:

Topological construct, Closure space, Extensional topological construct, Quasitopos, Cartesian closed category, Cartesian closed topological hull

Abstract

In the list of convenience properties for topological constructs the property of being a quasitopos is one of the most interesting ones for investigations in function spaces, differential calculus, functional analysis, homotopy theory, etc. The topological construct Cls of closure spaces and continuous maps is not a quasitopos. In this article we give an explicit description of the quasitopos topological hull of Cls using a method of F. Schwarz: we first describe the extensional topological hull of Cls and of this hull we construct the cartesian closed topological hull.

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Author Biographies

Veerle Claes, Vrije Universiteit Brussel

Departement Wiskunde

G. Sonck, Vrije Universiteit Brussel

Departement Wiskunde

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Published

2003-04-01

How to Cite

[1]
V. Claes and G. Sonck, “The quasitopos hull of the construct of closure spaces”, Appl. Gen. Topol., vol. 4, no. 1, pp. 15–24, Apr. 2003.

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Section

Regular Articles