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The article focuses on complements, counterexamples, and conjectures in the context of a topological form of the Gabriel-Rosenberg theorem for varieties characterized by constructible étale sheaves. Topics include the determination of the Zariski topological space of a scheme based on the category of constructible étale sheaves, analogues of Gabriel's reconstruction theorem, and examples illustrating inability to recover a field from Zariski topology of a projective space over a finite field.