AGM’s belief revision is one of the main paradigms in the study of belief change operations. Despite its popularity, it is well recognised that AGM’s work relies on a strong idealisation of the agent’s capabilities and on the supporting logic. Recent results in the literature have shed light on the definability of AGM-like belief change operations in general logics, showing how the properties of a logic can be leveraged to construct these operations. Exploring well-known connections between Logic, Algebra and Topology, our work explores a general notion of belief change contraction, which can be connected to well-studied operations in the literature, such as AGM rational contractions, partial meet contractions, and multiple contractions, employing the framework of Abstract Model Theory and Topological Semantics. We show that AGM rational contractions can be characterised in our framework, and we can establish connections to different results in the literature.