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Some new results on smoothness and rotundity in normed linear spaces

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References

  1. Banach, S., andS. Mazur: Zur Theorie der linearen Dimension. Studia Math.4, 100–112 (1933).

    Google Scholar 

  2. Bourbaki, N.: Espaces vectoriels topologiques. Act. Sci. Ind. no. 1189, Paris 1953.

  3. Choquet, G.: Existence des représentations intégrales dans les cones convexes. C. R. Acad. Sci. (Paris)243, 736–737 (1956).

    Google Scholar 

  4. Day, M. M.: Uniform convexity in factor and conjugate spaces. Ann. of Math. (2)45, 375–385 (1944).

    Google Scholar 

  5. Day, M. M.: Strict convexity and smoothness of normed spaces. Trans. Amer. Math. Soc.78, 516–528 (1955).

    Google Scholar 

  6. Day, M. M.: Normed linear spaces. Ergebn. Math. Grenz. no. 21, Berlin 1959.

  7. James, R. C.: Banach spaces with a specified number of separable conjugate spaces. Amer. math. Soc. Notices5, 680 (1958).

    Google Scholar 

  8. Klee, V.: Some characterizations of reflexivity. Rev. Ciencias (Lima)52, 15–23 (1950).

    Google Scholar 

  9. Klee, V.: Convex sets in linear spaces. Duke math. J.18, 443–466 (1951).

    Google Scholar 

  10. Klee, V.: Convex bodies and periodic homeomorphisms in Hilbert space. Trans. Amer. Math. Soc.74, 10–43 (1953).

    Google Scholar 

  11. Klee, V.: Some topological properties of convex sets. Trans. Amer. Math. Soc.78, 30–45 (1955).

    Google Scholar 

  12. Klee, V.: Separation properties of convex cones. Proc. Amer. Math. Soc.6, 313–318 (1955).

    Google Scholar 

  13. Klee, V.: Extremal structure of convex sets. II. Math. Z.69, 90–104 (1958).

    Google Scholar 

  14. Krein, M. G., andD. P. Milman: On extreme points of regular convex sets. Studia Math.9, 133–138 (1940).

    Google Scholar 

  15. Mazur, S.: Über die kleinste konvexe Menge, die eine gegebene kompakte Menge enthält. Studia Math.1, 83–85 (1929).

    Google Scholar 

  16. Mazur, S.: Über konvexe Mengen in linearen normierten Räumen. Studia Math.4, 70–84 (1933).

    Google Scholar 

  17. Michael, E.: Dense families of continuous selections. Fund. Math. (to appear).

  18. Poulsen, E. Th.: Compact convex sets with dense extreme points. Amer. Math. Monthly (to appear).

  19. Smulian, V. L.: On the principle of inclusion in the space of type (B). Mat. Sbornik (N. S.)5, 317 bis 328 (1939) (Russian).

    Google Scholar 

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National Science Foundation Senior Postdoctoral Fellow (U.S.A.), University of Washington (Seattle) and University of Copenhagen.

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Klee, V. Some new results on smoothness and rotundity in normed linear spaces. Math. Ann. 139, 51–63 (1959). https://doi.org/10.1007/BF01459822

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