In mathematics, particularly in topology, a filter is a collection of subsets of a given set that allows us to formalize the idea of convergence and limit points in a structured way. Filters help in defining continuity and limits of functions by providing a way to approach points in a topological space while capturing the notion of 'largeness' and 'eventuality' of sets in relation to other sets. They play a crucial role in characterizing continuous functions and their properties.
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