On convergence of topological aggregation functions

The concept of information aggregation is used in all scientific areas. More metric properties than required are often used when working with the mathematical concept of aggregation. This often gives the advantage of simplicity, but can sometimes obscure clues that might lead to a new discovery. Imprecision in space irregularities can be addressed by relaxing the metrizability condition using aggregation in a topological space. We study the convergence of nets of topological aggregation functions and their theoretical properties, and, in particular, the sensitivity of topological aggregation to input errors. It is clear that the underlying topology plays a crucial role in determining the aggregation properties.