This paper is devoted to the study of the topological dimension of the set of solutions of the operator inclusion of the form \(A(x)\in\lambda F(x)\), where A is a bounded linear surjective operator, and F is a multi-valued Lipschitz map with closed convex images. The resulting theorem establishes a connection between the dimension of the kernel of the operator A and the dimension of the set of solutions of this inclusion.

中文翻译：

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具有多值 Lipschitz 右手边的算子包含解集的拓扑性质

本文致力于研究形式为\(A(x)\in\lambda F(x)\)的算子包含的解集的拓扑维数，其中A是有界线性满射算子，并且F是具有封闭凸面图像的多值 Lipschitz 映射。由此产生的定理在算子A的核的维数和这个包含的解集的维数之间建立了联系。