Categorical Properties of Probabilistic Convergence Spaces

Authors: Herrlich H.1; Zhang D.2

Source: Applied Categorical Structures, Volume 6, Number 4, December 1998 , pp. 495-513(19)

Publisher: Springer

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Abstract:

The purpose of this paper is to discuss some categorical properties of probabilistic convergence spaces. Its main theses are: (1) the construct P-PrTop of probabilistic pretopological spaces is the extensional topological hull of the construct FTPcs of FT-diagonal probabilistic convergence spaces for every triangular norm T; (2) the construct P-PsTop of probabilistic pseudotopological spaces is the topological universe hull of FTPcs for every triangular norm T.

Keywords: topological construct; probabilistic convergence space; extensional topological hull; topological universe hull; Cartesian closed topological hull

Language: English

Document Type: Regular paper

Affiliations: 1: Fachbereich 3 Mathematik, University of Bremen, 28334 Bremen, Germany 2: Department of Mathematics, Sichuan University, Chengdu 610064, China

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