Can we identify Walrasian allocations? (Q1862641)

Using the framework of classical theory of economy the author transforms the question in the title skillfully to questions formulated with help of special topological spaces and then, using mathematically especially Fréchet ordering in topological spaces and first order optimality conditions, he can select economies, where an affirmative answer to the title question is possible. Normally, for the here considered infinite pure exchange economies the answer is negative.