Illinois Journal of Mathematics

Locally analytically connected topologies

Helen P. Wang

Full-text: Open access

Abstract

We shall prove the existence of two natural analytic topologies which refine the given topology on a space with a specified collection of continuous complex-valued functions. Whereas one would expect [2] the two constructions always, to yield the same analytic refinement, we show by example that is not the case.

This work was motivated by the search for analytic structure in the maximal ideal space of a function algebra, in particular the existence of nontrivial holomorphic mappings of analytic varieties into the maximal ideal space. (For restrictions on what type of analytic varieties need be considered, see Section 4.)

Article information

Source
Illinois J. Math., Volume 22, Issue 3 (1978), 443-448.

Dates
First available in Project Euclid: 20 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1256048606

Digital Object Identifier
doi:10.1215/ijm/1256048606

Mathematical Reviews number (MathSciNet)
MR497487

Zentralblatt MATH identifier
0469.46041

Subjects
Primary: 46G20: Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10]
Secondary: 46J20: Ideals, maximal ideals, boundaries 54C35: Function spaces [See also 46Exx, 58D15]

Citation

Wang, Helen P. Locally analytically connected topologies. Illinois J. Math. 22 (1978), no. 3, 443--448. doi:10.1215/ijm/1256048606. https://projecteuclid.org/euclid.ijm/1256048606


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