. . . "RIV/00216208:11320/12:10127428!RIV13-GA0-11320___" . . . . . "168147" . . "Singular points of order k of Clarke regular and arbitrary functions"@en . "P(GA201/09/0067), Z(MSM0021620839)" . . . "13"^^ . . "Hadamard derivative; singularities; Clarke regular functions"@en . "Let $X$ be a separable Banach space and $f$ a locally Lipschitz real function on $X$. Singular points of order $k$ of $f$ are those points at which the Clarke subdifferential of $f$ is at least $k$-dimensional. We prove that if $f$ is Clarke regu lar, then the set of all singular points of order $k$ of $f$ can be covered by countably many Lipchitz surfaces of codimension $k$. We prove also two results on arbitrary functions, which work with Hadamard directional derivatives and can be considered as generalization of the above result on Clarke regular functions."@en . "CZ - \u010Cesk\u00E1 republika" . . . . "53" . "Let $X$ be a separable Banach space and $f$ a locally Lipschitz real function on $X$. Singular points of order $k$ of $f$ are those points at which the Clarke subdifferential of $f$ is at least $k$-dimensional. We prove that if $f$ is Clarke regu lar, then the set of all singular points of order $k$ of $f$ can be covered by countably many Lipchitz surfaces of codimension $k$. We prove also two results on arbitrary functions, which work with Hadamard directional derivatives and can be considered as generalization of the above result on Clarke regular functions." . "Zaj\u00ED\u010Dek, Lud\u011Bk" . "Singular points of order k of Clarke regular and arbitrary functions"@en . . "RIV/00216208:11320/12:10127428" . "1" . "Singular points of order k of Clarke regular and arbitrary functions" . . "[13B9CF2B1E8A]" . "Singular points of order k of Clarke regular and arbitrary functions" . "1"^^ . "0010-2628" . "Commentationes Mathematicae Universitatis Carolinae" . "1"^^ . . . "11320" .