Banach analytic structures on metrizable topological spaces and a cancellation problem

Let X be a topological space whose topology may be defined by a complete metric. Douady (case X compact) and Pestov (the general case) proved that X may be equipped with a structure of Banach analytic set. Here we prove that if X is not discrete, then this may be done in uncountably many ways. Let (...

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Bibliographic Details
Published inComplex variables and elliptic equations Vol. 51; no. 2; pp. 105 - 108
Main Author Ballico, E.
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.02.2006
Subjects
1991 Mathematics and Subject Classifications
Banach analytic set
Bounded holomorphic functions
Cancellation problem
Complex structure
Infinite-dimensional analytic set
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Summary:Let X be a topological space whose topology may be defined by a complete metric. Douady (case X compact) and Pestov (the general case) proved that X may be equipped with a structure of Banach analytic set. Here we prove that if X is not discrete, then this may be done in uncountably many ways. Let ( Y, d ) be a non-complete metric space and its completion. Here we prove that we may see as a closed analytic subset of a Banach space in such a way that with V a dense linear subspace of . Then we will prove (using bounded holomorphic functions) the following result. Let X be a connected open subset of an infinite-dimensional locally convex topological vector space V with the weak topology and A an open domain of such that has positive capacity. Then X × A is not biholomorphic to X.
ISSN:1747-6933
1747-6941
DOI:10.1080/02781070500369339