Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 10, Number 2 (2019), 284-290.
The Tychonoff theorem and invariant pseudodistances
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 of convex domains in a complex, locally convex, Hausdorff, and infinite-dimensional topological vector space is approximated by the Carathéodory distances in finite-dimensional linear subspaces . Originally this result is due to Dineen, Timoney, and Vigué who apply ultrafilters in their proof.
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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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