Research

• Constructive Topology: especially development of the theory of Bishop spaces, a function-theoretic approach to general topology within BISH^*, where BISH^* is Bishop's informal system of constructive mathematics BISH equipped with inductive definitions with rules of countably many premisses.
• Constructive Analysis.
• Constructive Lipschitz Analysis: study of the role of Lipschitz functions in constructive analysis and of the extension theorems of Lipschitz functions (McShane-Whitney extension theorem, Kirszbraun theorem) within BISH.
• Constructive Combinatorics.
• Constructive Computability Theory at Higher Types.
• Brouwer's Intuitionism.
• Euclidean and Non-Euclidean Geometries.
• Homotopy Type Theory.
• Formalization of mathematics using the proof-assistant Minlog.

Last modified: 30.06.2017