Evaluation maps on products of separable metrizable spaces are Borel

• Autores: Roman Pol
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 32, Nº 4, 2006, págs. 1191-1196
• Idioma: inglés
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• Resumen

  • Given a completely regular space X we denote by C(X) the space of continuous real - valued functions on X, and let e : X×C(X) ? R, e(x,f) = f(x), be the evaluation map. The function space C(X) is considered with the pointwise topology. We prove the result stated in the title, and give an example of a compact separable space X such that the evaluation map e on X is Borel measurable, but the preimage of some open set under e is not a countable union of closed sets, answering two questions by M.R.Burke, Borel measurability of separately continuous functions II, Top. Appl. 134 (2003), 154 - 188.