Topology is defined as the arrangement of relations within a system. This paper establishes that system behavior is not determined solely by components or interaction rules, but by how those components are connected. The topology of a system shapes how signals move, how influence propagates, and how outcomes emerge, even when all other conditions remain the same. It explains why systems with identical elements and constraints can behave differently due to differences in how their relations are arranged. The concept is introduced in a domain-independent manner and applies across physical, biological, cognitive, and computational systems. It provides a basis for understanding how pathways of connection influence stability, variation, and the propagation of change. This paper defines topology as a structural layer of arrangement and does not extend into classification, optimization, or design of specific configurations.