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Graham Manuell - 3/ 无点拓扑与构造主义数学
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https://youtu.be/yHCEFKdi6oA 2024-08-27 - NITheCS & SU Category Theory Research Seminar Workshop on pointfree topology and constructive mathematics - part 3 Dr Graham Manuell (Stellenbosch University) ABSTRACT Constructive logic is a generalisation of classical logic that applies in more situations, including mathematical universes (toposes) where propositions can take different values at different locations in some space or where every function from ℕ to ℕ is computable. Unfortunately, in this general setting many classical results of point-set topology fail. However, almost all of these results can be recovered if we reformulate topology in terms of lattices of opens without predefined underlying sets of points. Moreover, this perspective also sheds light on many not-obviously-topological aspects of constructive mathematics itself. In this third lecture, I will describe the construction of free frames and introduce sublocales. Along the way we will also see that finiteness can be quite subtle in constructive mathematics, but can be understood by analogy to some topological concepts. BIOGRAPHY Graham Manuell is a lecturer at Stellenbosch University. His research interests include pointfree topology, category theory, constructive mathematics and semigroup theory.
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