Skip to main content
Log in

Leray-Schauder theory without local convexity

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Altman, M.: An extension to locally convex spaces of Borsuk's theorem on antipodes. Bull. Acad. Polon. Sci.6, 293–295 (1958).

    Google Scholar 

  2. Altman, M.: Continuous transformations of open sets in locally convex spaces. Bull. Acad. Polon. Sci.6, 297–301 (1958).

    Google Scholar 

  3. Borsuk, K.: Drei Sätze über dien-dimensionale Euklidische Sphäre. Fundamenta Math.20, 177–190 (1933).

    Google Scholar 

  4. Bourbaki, N.: Espaces vetoriels topologiques. Chaps. I–II, Actualités Scientifique et Industrielles, No. 1189. Paris 1953.

  5. Dugundji, J.: An extension of Tietze's theorem. Pacific J. Math.1, 353–367 (1951).

    Google Scholar 

  6. Granas, A.: Extension homotopy theorem in Banach spaces and some of its applications to the theory of nonlinear equations (Russian with English summary). Bull. Acad. Polon. Sci.7, 387–394 (1959).

    Google Scholar 

  7. Klee, Victor: Shrinkable neighborhoods in Hausdorff linear spaces. Math. Ann.141, 281–285 (1960).

    Google Scholar 

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

    Google Scholar 

  9. Leray, J.: La théorie des points fixes et ses applications en analyse. Proc. Int. Congress Math., Cambridge, Mass.2, 202–208 (1950).

    Google Scholar 

  10. Leray, J., andJ. Schauder: Topologie et équations fonctionelles. Ann. sci. école norm. super. (3)51, 45–78 (1934).

    Google Scholar 

  11. Markouchevitz, A. I.: Certain questions in the theory of approximation and expansion of functions in series (Russian). Doctoral dissertation, 1944.

  12. Michael, Ernest: Some extension theorems for continuous functions. Pacific J. Math.3, 789–806 (1953).

    Google Scholar 

  13. Michael, Ernest: Continuous selections I. Ann. Math. (2)63, 361–382 (1956).

    Google Scholar 

  14. Nagumo, Mitio: Degree of mapping in convex linear topological spaces. Am. J. Math.73, 497–511 (1951).

    Google Scholar 

  15. Nikol'skii, V. N.: Best approximation and basis in a Frechet space (Russian). Doklady Akad. Nauk S.S.S.R. (N. S.)59, 639–642 (1948).

    Google Scholar 

  16. Ptak, Vlastimil: Weak compactness in convex topological linear spaces. Czechoslov. Math. J.4, 175–186 (1954).

    Google Scholar 

  17. Robertson, Wendy: Completions of topological vector spaces. Proc. London Math. Soc. (3)8, 242–257 (1958).

    Google Scholar 

  18. Schauder, J.: Der Fixpunktsatz in Funktionalräumen. Studia Math.2, 171–180 (1930).

    Google Scholar 

  19. Tychonoff, A.: Ein Fixpunktsatz. Math. Ann.111, 767–776 (1935).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Research fellow of the Alfred P. Sloan Foundation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Klee, V. Leray-Schauder theory without local convexity. Math. Ann. 141, 286–296 (1960). https://doi.org/10.1007/BF01360763

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01360763

Keywords

Navigation