Locality (mathematics)

In mathematics, especially in topology and analysis, locality refers to the idea that the properties or behavior of a mathematical object—such as a function, space, or structure—depend primarily on its immediate surroundings or small regions. Essentially, a property is local if knowing it in small neighborhoods around each point allows us to understand or determine the property for the entire object. This concept helps mathematicians analyze complex structures by breaking them down into simpler, manageable parts, focusing on how things behave within small, focused areas rather than the entire universe at once.