Intuitionistic overlap structures
DOI:
https://doi.org/10.12775/LLP.2013.011Keywords
overlap algebras, connection structures, mereological fields, constructive reasoningAbstract
We study some connections between two kinds of \emph{overlap} relations: that of point-free geometries in the sense of Grzegorczyk, Whitehead and Clarke, and that recently introduced by Sambin within his constructive approach to topology. The main thesis of this paper is that the overlap relation in the latter sense is a necessary tool for a constructive and intuitionistic development of point-free geometry.
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