On the Borel complexity and the complete metrizability of spaces of metrics
Copyright policy )On the Borel complexity and the complete metrizability of spaces of metrics
Abstract Given a metrizable space X X , let A M ( X ) AM\left(X) be the space of continuous bounded admissible metrics on X X , which is endowed with the sup-metric. In this article, we shall investigate the Borel complexity and the complete metrizability of A M ( X ) AM\left(X) and show that a separable metrizable space X X is σ \sigma -compact if and only if A M ( X ) AM\left(X) is completely metrizable.
- Kanagawa University Japan
- Berlin Central and Regional Library Germany
absolute borel class, completely metrizable, QA299.6-433, Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets), General Topology (math.GN), complete metrizability, absolute Borel classes, Function spaces in general topology, Sonstiges, Metric spaces, metrizability, Mathematik, spaces of admissible metrics, admissible metric, 54h05, FOS: Mathematics, sup-metric, primary 54c35, secondary 54e35, Analysis, Mathematics - General Topology
absolute borel class, completely metrizable, QA299.6-433, Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets), General Topology (math.GN), complete metrizability, absolute Borel classes, Function spaces in general topology, Sonstiges, Metric spaces, metrizability, Mathematik, spaces of admissible metrics, admissible metric, 54h05, FOS: Mathematics, sup-metric, primary 54c35, secondary 54e35, Analysis, Mathematics - General Topology
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