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Summability in topological spaces. (English) Zbl 1216.40009
Summary: The main purpose of the paper is to introduce the notion of summability in abstract Hausdorff topological spaces. We give a characterization of such summability methods when the space allows a countable base. We also provide several Tauberian theorems in topological structures. Some open problems are discussed.

##### MSC:
 40J05 Summability in abstract structures (should also be assigned at least one other classification number from Section 40-XX) 40E05 Tauberian theorems, general
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