Conditionally complete sponges: new results on generalized lattices
Metric Geometry
2018-04-20 v1
Abstract
Sponges were recently proposed as a generalization of lattices, focussing on joins/meets of sets, while letting go of associativity/transitivity. In this work we provide tools for characterizing and constructing sponges on metric spaces and groups. These are then used in a characterization of epigraph sponges: a new class of sponges on Hilbert spaces whose sets of left/right bounds are formed by the epigraph of a rotationally symmetric function. We also show that the so-called hyperbolic sponge generalizes to more than two dimensions.
Cite
@article{arxiv.1804.07281,
title = {Conditionally complete sponges: new results on generalized lattices},
author = {Jasper J. van de Gronde and Wim H. Hesselink},
journal= {arXiv preprint arXiv:1804.07281},
year = {2018}
}
Comments
24 pages