As seen, for instance, in "Survey on Singularities and Differential Algebras of Generalized Functions : A Basic Dichotomic Sheaf Theoretic Singularity Test", http://hal.archives-ouvertes.fr/hal-00510751, it appears that spaces of generalized functions have to be flabby sheaves in order for their elements to be able to contain singularities in large classes. The well known Schwartz distributions, as an example, are not flabby sheaves, this seemingly being the reason they cannot accommodate analytic functions with essential singularities, among others. Question : is indeed the property of being flabby sheaves which makes spaces of generalized functions have elements with singularities that belong to the largest possible classes ?
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