We consider the concept images of open sets in a metric space setting held by some Pure Mathematics students in the penultimate year of their undergraduate degree. Ten students were interviewed and asked to define the concept of an open set, as well as to work on some specially designed mathematical tasks on this topic. The analysis of the interview data revealed five main categories of concept image of open sets based on: the formal definition; the idea of boundary of sets; open sets in Euclidean space; the union of open balls; visualisation.