convergence structures

Convergence structures are a way of describing how sequences or collections of objects, like points or functions, approach a specific limit or goal within a mathematical space. They provide a formal framework to understand different modes of "getting closer," such as pointwise, uniform, or more general types of convergence. Essentially, they define rules for when a sequence can be considered to be approaching a particular element, helping mathematicians analyze and compare behaviors across various contexts in a consistent way.