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\title[Summability in Topological Spaces]
      {Summability in Topological Spaces}

\author{H. Cakalli and M.K. Khan}
\address{Department of Mathematical Sciences, Kent State University,
         Kent, OH}
\email{kazim@math.kent.edu}


\begin{abstract}
The main purpose of the talk is to consider the
notion of summability in abstract Hausdorff topological
spaces so that the purely topological notions and purely
summability notions could be separated. We give a
characterization of such summability
methods when the toplogical space allows a countable base.
We also provide several invariant Tauberian theorems in
topological structures. Some open problems are discussed.
\end{abstract}

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