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Morphisms of Klein Surfaces and Stoilow’s Topological Theory of Analytic Functions

In: Deformations of Mathematical Structures

Author

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  • Cabiria Andreian Cazacu

    (University of Bucharest, Faculty of Mathematics)

Abstract

It is proved (Theorem 1) that for every surface X (orientable or non-orientable, with border or without) there exists an interior transformation T: X → D, where D denotes the closed disc. The Klein covering (X, T, D) is shown to be complete and it can present folds on 3D. This generalizes the Stoilow theorem that for every orientable surface X without border there exists an interior transformation T:X→S. The generalized theorem is then applied to prove the existence of a dianalytic structure on every surface (Theorem 2).

Suggested Citation

  • Cabiria Andreian Cazacu, 1989. "Morphisms of Klein Surfaces and Stoilow’s Topological Theory of Analytic Functions," Springer Books, in: Julian Ławrynowicz (ed.), Deformations of Mathematical Structures, pages 235-246, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-2643-1_22
    DOI: 10.1007/978-94-009-2643-1_22
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