Abstract
The notion of a completely saturated packing [Monats. Math. 125 (1998) 127-145] is a sharper version of maximum density, and the analogous notion of a completely reduced covering is a sharper version of minimum density. We define two related notions: uniformly recurrent and weakly recurrent dense packings, and diffusively dominant packings. Every compact domain in Euclidean space has a uniformly recurrent dense packing. If the domain self-nests, such a packing is limit-equivalent to a completely saturated one. Diffusive dominance is yet sharper than complete saturation and leads to a better understanding of –saturation.
Citation
Greg Kuperberg. "Notions of denseness." Geom. Topol. 4 (1) 277 - 292, 2000. https://doi.org/10.2140/gt.2000.4.277
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