Positive Topology

Giovanni Sambin has been doing research in logic and the foundations of mathematics since the 1970s. He is among the founders of provability logic and has been developing the field of topology since the 1990s, adopting a dynamic view in mathematical practice, leading to positive topology, a new, richer approach to constructive topology based on a dynamic vision of the nature of mathematics. He was the first president of the Italian Association of Logic and its Applications (AILA).

• Preface About This Book 1: Dynamic Constructivism: A New Conception of Mathematics 2: The Minimalist Foundation: Basic Notions and Tools 3: Basic Pairs: Symmetry and Duality in Topology 4: Relation-Pairs: Continuity is a Commutative Square 5: Concrete Spaces: Benefits of Keeping a Base 6: Convergent Relation-Pairs: Towards Topology With Points 7: Basic Topologies: Pointfree Topology Without Convergence 8: Continuous Relations: Respecting Covers and Positivities 9: Positive Topologies and Formal Maps: Pointfree Topology 10: Ideal Spaces and Maps: Ideal Aspects Over Real Topology 11: Topological Systems: a Place for all Topological Notions 12: Overlap Algebras: the Power of a Set as an Algebra 13: Overlap Topologies: Putting Topology in Algebraic Terms Appendix A: Generating Positivity By Co-induction References Index