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Mathematics - Geometry & Topology | Topology on Spaces of Holomorphic Mappings

Topology on Spaces of Holomorphic Mappings

Nachbin, Leopoldo

Softcover reprint of the original 1st ed. 1969, VIII, 68 p.

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  • About this textbook

The present report on spaces of holomorphic mappings was prepared for the Sexto Coloquio Brasileiro de Matematica (Po~os de Caldas, Minas Gerais, Brazil, July 1967). I also had the oppor­ tunity of giving a series of lectures on this material while I was a visiting member at the Center for Theoretical Studies of the University of Miami (Coral Gables, Florida, USA, February 1968). The preparation of this report was sponsored in part by the USA National Science Foundation through a grant to the University of Rochester. I am glad to thank Professors Paul R. Halmos and Peter J. Hilton for accepting my text as part of the series Ergebnisse der Mathematik und ihre Grenzgebiete. Rochester, New York 1968 Leopoldo Nachbin Contents § 1. Introduction. 1 § 2. Notation and Terminology 4 § 3. Continuous Polynomials 6 § 4. Convergent Power Series 11 § 5. Holomorphic Mappings. 16 § 6. The Cauchy Integral 20 § 7. Convergence of Taylor Series. 26 § 8. Topology on the Space of all Holomorphic Mappings 31 § 9. Holomorphy Types. 34 § 10. Differentiation of Holomorphy Types . 38 § II. Topology on Spaces of Holomorphic Mappings. 43 § 12. Bounded Subsets. 49 § 13. Relatively Compact Subsets . 54 § 14. The Current Holomorphy Type 59 § 15. Bibliographical References. 62 Subject Index 65 § 1.

Content Level » Research

Keywords » Holomorphe Abbildung - Lokalkonvexer Vektorraum - Mappings - Topology

Related subjects » Geometry & Topology

Table of contents 

§ 1. Introduction.- § 2. Notation and Terminology.- § 3. Continuous Polynomials.- § 4. Convergent Power Series.- § 5. Holomorphic Mappings.- § 6. The Cauchy Integral.- § 7. Convergence of Taylor Series.- § 8. Topology on the Space of all Holomorphic Mappings.- § 9. Holomorphy Types.- § 10. Differentiation of Holomorphy Types.- § 11. Topology on Spaces of Holomorphic Mappings.- § 12. Bounded Subsets.- § 13. Relatively Compact Subsets.- § 14. The Current Holomorphy Type.- § 15. Bibliographical References.

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