6533b86efe1ef96bd12cb611

RESEARCH PRODUCT

Finitary formal topologies and Stone’s representation theorem

Giovanni SambinFrancesco Ciraulo

subject

Stone's representationGeneral Computer ScienceRelation (database)Representation theoremFormal topologyformal topology; positivity; Stone's representation; constructive methodsPositivityBasis (universal algebra)Topological spaceStone’s representationMathematical proofConstructiveTheoretical Computer ScienceConstructive methodsAlgebraDistributive propertyFinitaryComputer Science(all)Mathematics

description

AbstractWe study the concept of finitary formal topology, a point-free version of a topological space with a basis of compact open subsets. The notion of finitary formal topology is defined from the perspective of the Basic Picture (introduced by the second author) and thus it is endowed with a binary positivity relation. As an application, we prove a constructive version of Stone’s representation theorem for distributive lattices. We work within the framework of a minimalist foundation (as proposed by Maria Emilia Maietti and the second author). Both inductive and co-inductive methods are used in most proofs.

yearjournalcountryeditionlanguage
2008-10-01Theoretical Computer Science
https://doi.org/10.1016/j.tcs.2008.06.020