Modes of convergence (annotated index)

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The purpose of this article is to serve as an annotated index of various modes of convergence and their logical relationships. For an expository article, see Modes of convergence. Simple logical relationships between different modes of convergence are indicated (e.g., if one implies another), formulaically rather than in prose for quick reference, and indepth descriptions and discussions are reserved for their respective articles.

Guide to this index. To avoid excessive verbiage, note that each of the following types of objects is a special case of types preceding it: sets, topological spaces, uniform spaces, topological abelian groups (TAG), normed vector spaces, Euclidean spaces, and the real/complex numbers. Also note that any metric space is a uniform space. Finally, subheadings will always indicate special cases of their super headings.

The following is a list of modes of convergence for: