1. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. © Continuities Of Metric Projection And Geometric Consequences Huotari, R; Li, W ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS, JOURNAL OF APPROXIMATION THEORY; pp: 319-339; Vol: 90 King Fahd University of Petroleum & Minerals http://www.kfupm.edu.sa Summary We discuss the geometric characterization of a subset K of a normed linear space via continuity conditions on the metric projection onto K. The geometric properties considered include convexity, tubularity, and polyhedral structure. The continuity conditions utilized include semicontinuity, generalized strong uniqueness and the non- triviality of the derived mapping. In finite-dimensional space with the uniform norm we show that convexity is equivalent to rotation-invariant almost convexity and we characterize those sets every rotation of which has continuous metric projection. We show that polyhedral structure underlies generalized strong uniqueness of the metric projection. (C) 1997 Academic Press, Inc. References: BALAGANSKII VS, APPROXIMATIVE GEOMET BALAGANSKII VS, 1982, MATH NOTES+, V31, P397 BISHOP E, 1961, B AM MATH SOC, V67, P97 BJORNESTAL BO, 1979, APPROXIMATION THEORY, V4, P43 BLATTER J, 1968, MATH ANN, V178, P12 BLATTER J, 1969, REV ROUMAINE MATH PU, V14, P615 BRAESS D, 1986, NONLINEAR APPROXIMAT BROWN AL, 1964, P LOND MATH SOC, V14, P577 BROWN AL, 1971, J FUNCT ANAL, V8, P431 BROWN AL, 1989, J APPROX THEORY, V57, P48 BUNT LNH, 1934, THESIS U GRONINGEN A BURKE JV, 1993, SIAM J CONTROL OPTIM, V31, P1340 CHENEY EW, 1982, INTRO APPROXIMATION DEUTSCH F, 1988, J APPROX THEORY, V53, P266 DEUTSCH F, 1991, J APPROX THEORY, V66, P198 DEUTSCH F, 1993, TOPICS POLYNOMIALS O, P143 EKELAND I, 1974, J MATH ANAL APPL, V47, P324 Copyright: King Fahd University of Petroleum & Minerals; http://www.kfupm.edu.sa

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