Abstract
LetC (E) be the space of real-valued continuous functions on a locally compact metric spaceE without isolated points, endowed with the uniform metric. The structure of sections of typical functions from C(E) in the sense of Baire's category is studied by functions of Lipschitz type. In particular, it is proved forE, which is generally not endowed by a linear structure, that a theorem is valid which, in the particular case ofE=[0, 1], implies a well-known result, due to Jarnik, on subdifferential numbers of a typical continuous function on a closed interval.
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