I. E. Schochetman, S. K. Tsui, "On the lattice theory of function semi-norms", International Journal of Mathematics and Mathematical Sciences, vol. 6, Article ID 796980, 17 pages, 1983. https://doi.org/10.1155/S0161171283000381
On the lattice theory of function semi-norms
We consider the lattice of function semi-norms over a measure space, as well as certain distinguished subsets. We determine which subsets are sublattices and, in turn, which of these are Dedekind complete. We also investigate the extent to which the distributive and DeMorgan Laws are valid in this setting.
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