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Semi-continuity of metric projections in  -direct sums |
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| Authors: | V Indumathi |
| Institution: | Department of Mathematics, Pondicherry University, Kalapet, Pondicherry-605014, India |
| Abstract: | Let  be a proximinal subspace of finite codimension of  . We show that  is proximinal in  and the metric projection from  onto  is Hausdorff metric continuous. In particular, this implies that the metric projection from  onto  is both lower Hausdorff semi-continuous and upper Hausdorff semi-continuous. |
| Keywords: | Proximinal metric projection lower semi-continuity upper Hausdorff semi-continuity |
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