Annals of Functional Analysis

The Tychonoff theorem and invariant pseudodistances

Tadeusz Kuczumow and Stanisław Prus

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Carathéodory pseudodistance Kobayashi pseudodistance Tychonoff theorem


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.

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