The set of universal and ultrahomogeneous retractions on the Urysohn space is characterized topologically via a new extension property (UR*) equivalent to those features and a new pointwise retract topology, yielding results on its Borel complexity and density.
Kubi\'s , Metric-enriched categories and approximate Fra\" ss\' e limits , preprint, arxiv.org/abs/1210.6506 https://arxiv.org/abs/1210.6506
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Topological size of the set of universal and ultrahomogeneous retractions on the Urysohn space
The set of universal and ultrahomogeneous retractions on the Urysohn space is characterized topologically via a new extension property (UR*) equivalent to those features and a new pointwise retract topology, yielding results on its Borel complexity and density.