Constructive mathematics replaces abstract existence claims with explicit constructions and allows for the broader application of mathematical results. Unfortunately, many standard theorems of analysis and topology fail in their usual form. Pointfree topology, which studies spaces via their lattices of opens, resolves these difficulties and allows us to recover constructive versions of classical results together with new consequences. We hope these notes will provide an accessible introduction to the subject.

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Pointfree Topology and Constructive Mathematics

  • Graham Manuell

摘要

Constructive mathematics replaces abstract existence claims with explicit constructions and allows for the broader application of mathematical results. Unfortunately, many standard theorems of analysis and topology fail in their usual form. Pointfree topology, which studies spaces via their lattices of opens, resolves these difficulties and allows us to recover constructive versions of classical results together with new consequences. We hope these notes will provide an accessible introduction to the subject.