Some points in formal topology

1 Some remarks, some results 5 1.1 The point of formal topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 A formal topology is. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 A summary of developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.1 A toolbox to do mathematics in type theory . . . . . . . . . . . . . . . . . . 9 1.3.2 Predicative completeness proofs . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3.3 Predicative presentation of frames . . . . . . . . . . . . . . . . . . . . . . . 11 1.3.4 Domain theory as a branch of formal topology . . . . . . . . . . . . . . . . 12 1.3.5 Inductive generation of formal topologies and proof-theoretic methods . . . 13 1.3.6 The continuum as a formal space . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3.7 Classical theorems constructivized . . . . . . . . . . . . . . . . . . . . . . . 14