In this lecture notes, we study lters and limits in a feasible sufficiently general way for many applications to Physics, Economics and Social Science. In particular we analyze: Filters; Filter bases; Basic example in topological spaces; Basic examples in preordered spaces; Filtered spaces; Induced filter bases; Examples in topological spaces; Examples on the real line; Limits; Limits with respect to filter bases; Limits with respect to filter bases on subspaces; Limits and topology; Limits of functions on topological spaces; Limits of functions on a topological subspace; Some basic theorems for topology; Unicity of the limit in Hausdor spaces; Limits and functionals; Limits for real functional; Limits and operations; Local boundness; Complements; Limits and convergence of filtered bases; Limit of composition.

Filters and limits in filtered spaces

David Carfì
2017-01-01

Abstract

In this lecture notes, we study lters and limits in a feasible sufficiently general way for many applications to Physics, Economics and Social Science. In particular we analyze: Filters; Filter bases; Basic example in topological spaces; Basic examples in preordered spaces; Filtered spaces; Induced filter bases; Examples in topological spaces; Examples on the real line; Limits; Limits with respect to filter bases; Limits with respect to filter bases on subspaces; Limits and topology; Limits of functions on topological spaces; Limits of functions on a topological subspace; Some basic theorems for topology; Unicity of the limit in Hausdor spaces; Limits and functionals; Limits for real functional; Limits and operations; Local boundness; Complements; Limits and convergence of filtered bases; Limit of composition.
2017
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/3122067
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