International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 3, Pages 431-447
doi:10.1155/S0161171283000381
On the lattice theory of function semi-norms
I.E. Schochetman
and S.K. Tsui
Department of Mathematical Sciences, Oakland University, Rochester 48063, Michigan, USA
Abstract
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.