The Tychonoff theorem and invariant pseudodistances

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 Caratheodory distance cD of convex domains D in a complex, locally convex, Hausdorff, and infinite-dimensional topological vector space is approximated by the Caratheodory distances cD∩Y in finite-dimensional linear subspaces Y. Originally this result is due to Dineen, Timoney, and Vigue who apply ultrafilters in their proof.