We give some topological properties of the generalized Clarke subdifferential which is an extension of the notion of the Clarke subdifferentiability [5]. Potential advantages of generalized Clarke subdifferential over other concepts of subdifferentiability might be related to the fact that it offers a rich calculus and applications. It allows us, for example, to present a convenient test for the weak metric regularity of mappings non-necessarily strictly Fréchet differentiable.
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