The ultrametrization map U is 1-Lipschitz on all metric spaces, preserves products with dotted connected spaces, and forces mutual exclusion of ultrametric and dotted connected spaces in unbounded clouds.
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Ultrametric spaces and clouds
The ultrametrization map U is 1-Lipschitz on all metric spaces, preserves products with dotted connected spaces, and forces mutual exclusion of ultrametric and dotted connected spaces in unbounded clouds.