This chapter considers the role of topology in logic programming semantics. There is a history of topology being used in computer science in general, much of it stemming from the role of the Scott topology in domain theory and in conventional programming language semantics. The chapter explores the role of topology in finding models for logic programs and its role as a foundational framework for logic programming semantics. There are two main topologies which have important properties in relation to logic programming semantics, namely, the well-known Scott topology and a topology, called the Cantor topology, which has connections with the Scott topology. Indeed, convergence spaces and convergence classes are to a considerable extent appropriate structures with which to investigate semantical questions in computer science in general and in logic programming in particular. Order is not a satisfactory foundation for the semantics of logic programming languages in the presence of negation, and yet negation is a natural part of most logics.