Abstract
An analog of the finite-dimensional theorem about the upper semicontinuity of the geometric difference of continuous multivalued maps for separable Banach spaces is obtained. Sufficient conditions for the continuity of the geometric difference of multivalued maps in finite-dimensional spaces without the “nonempty interior” condition are obtained. Examples that demonstrate the unimprovability of these results are given.
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Balashov, M.V. Geometric Difference of Multivalued Maps. Mathematical Notes 70, 147–153 (2001). https://doi.org/10.1023/A:1010242406096
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DOI: https://doi.org/10.1023/A:1010242406096