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International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 1, Pages 17-22

Functorial properties of the lattice of functional semi-norms

Oakland University, Rochester 48063, Michigan, USA

Received 10 August 1984

Copyright © 1986 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.