International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 1, Pages 17-22
doi:10.1155/S0161171286000029

Functorial properties of the lattice of functional semi-norms

Abstract

Given a measureable transformation between measure spaces, we determine when such gives rise to a mapping between the corresponding lattice of function semi-norms. We further determine when this mappings preserves norms and observe that it does preserve certain other important properties. We next establish a functorial connection between measure spaces and lattice. Finally, we show that the above lattice mapping does not commute with the associate construction.