Annals of Functional Analysis

The Tychonoff theorem and invariant pseudodistances

Tadeusz Kuczumow and Stanisław Prus

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Abstract

In this article we introduce a method of constructing functions with claimed properties by using the Tychonoff theorem. As an application of this method we show that the Carathéodory distance cD of convex domains D in a complex, locally convex, Hausdorff, and infinite-dimensional topological vector space is approximated by the Carathéodory distances cDY in finite-dimensional linear subspaces Y. Originally this result is due to Dineen, Timoney, and Vigué who apply ultrafilters in their proof.

Article information

Source
Ann. Funct. Anal., Volume 10, Number 2 (2019), 284-290.

Dates
Received: 15 September 2018
Accepted: 29 October 2018
First available in Project Euclid: 22 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.afa/1553241618

Digital Object Identifier
doi:10.1215/20088752-2018-0029

Mathematical Reviews number (MathSciNet)
MR3941389

Zentralblatt MATH identifier
07083896

Subjects
Primary: 46G20: Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10]
Secondary: 32F45: Invariant metrics and pseudodistances

Keywords
Carathéodory pseudodistance Kobayashi pseudodistance Tychonoff theorem

Citation

Kuczumow, Tadeusz; Prus, Stanisław. The Tychonoff theorem and invariant pseudodistances. Ann. Funct. Anal. 10 (2019), no. 2, 284--290. doi:10.1215/20088752-2018-0029. https://projecteuclid.org/euclid.afa/1553241618


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References

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