Summary: A mathematical model of knowledge base revision attempts to faithfully capture an intuitive notion of `closest' new information relative to some given background information. An attempt to topologically characterize this notion of closest information leads naturally to an approach using non-monotonic exterior operators in contrast to standard monotonic interior or closure operators. This paper introduces exterior topology and uses it to create revision spaces. It is shown that a generalized AGM revision algebra may be characterized in terms of a suitable family of revision spaces and that symmetric revision spaces induced by a distance function provide a metric notion of theory change.