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Yayın Summability in topological spaces(PERGAMON-ELSEVIER SCIENCE LTD, 2011) Cakalli, H.; Khan, M. K.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. (C) 2010 Elsevier Ltd. All rights reserved.