Towards a theory of contextual topology (Q2743186)

This PhD thesis discusses the interplay between Formal Concept Analysis and topology. The thesis is structured in five chapters and two appendices. Chapter 1 recalls the main definitions and results of Formal Concept Analysis. In Chapter 2 and Appendix 2, Formal Concept Analysis (i.e., more specifically its knowledge acquisition technique Attribute Exploration) is used for a systematic analysis of the main notions of topology. In Chapter 3, first the notion of a topological context (as introduced by G. Hartung) is recalled. It introduces the idea of approximation to Formal Concept Analysis, and can be used for a representation theory of bounded lattices. Then the approach is extended to double Boolean algebras (as introduced by R. Wille), based on representation results for polarity lattices. The latter are joint work of the author with G. Hartung and M. Kamara, which is presented in Appendix 1. Chapters 4 and 5 follow then another approach to approximation in Formal Concept Analysis by considering a (pseudo-)metric on formal contexts, which can be lifted to the concept lattice. The thesis extends the foundations of a theory of contextual topology, thereby opening a broad range of stimulating research questions.