On linear operators extending [pseudo]metrics

Details On linear operators extending [pseudo]metrics On linear operators extending [pseudo]metrics

2012-02-07

arxiv.org/abs/1202.1381v1

Bull. Polish Acad. Sci. Math. 48:1 (2000) 201-208

Mathematics

General Topology

8 pages

Scientific paper

For every closed subset $X$ of a stratifiable [resp. metrizable] space $Y$ we construct a positive linear extension operator $T:R^{X\times X}\to R^{Y\times Y}$ preserving constant functions, bounded functions, continuous functions, pseudometrics, metrics, [resp. dominating metrics, and admissible metrics]. This operator is continuous with respect to each of the three topologies: point-wise convergence, uniform, and compact-open. An equivariant analog of the above statement is proved as well.

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