A universal complex structure on complete metrizable topological spaces

Let X be a topological space whose topology may be defined by a complete metric d. Taking all such metrics d we define a universal complex structure on X. For this complex structure the sheaf of germs of holomorphic functions on X coincides with the sheaf of germs of continuous functions on X, and h...

Full description

Saved in:
Bibliographic Details
Published inComplex variables, theory & application Vol. 49; no. 5; pp. 319 - 321
Main Author Ballico, E.
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 15.04.2004
Subjects
1991 Mathematics Subject Classifications: 32K05
Banach analytic set
Complex structure
Infinite-dimensional analytic set
Online AccessGet full text

Cover

More Information
Summary:Let X be a topological space whose topology may be defined by a complete metric d. Taking all such metrics d we define a universal complex structure on X. For this complex structure the sheaf of germs of holomorphic functions on X coincides with the sheaf of germs of continuous functions on X, and hence the theories of topological and holomorphic vector bundles on X are the same.
ISSN:0278-1077
1563-5066
DOI:10.1080/02781070410001701047