Syllabus
Special lattices, algebraic aspects. Boolean and Heyting algebras.
Partial orders with suprema of directed sets (DCPO), their role in computer science. Continuous and algebraic lattices and posets. Scott information systems and domains. Categories of domains.
Fundamentals of topology. Spaces and continuous maps. Separation axioms. Compactness. Special topologies of computer science (Scott, Lawson).
Fundamentals of point-free topology: concepts and basic facts, relation ot classical topology, constructive aspects.
Annotation
Partial order, special partial orders in computer science. DCPOs, domains.
Continuous and algebraic posets. Introduction to topology.