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International Journal of Mathematics and Mathematical Sciences
Volume 3, Issue 3, Pages 433-443
http://dx.doi.org/10.1155/S0161171280000312

Properties of complements in the lattice of convergence structures

Department of Mathematics, Cameron University, Lawton 73505, Oklahoma, USA

Received 11 October 1979

Copyright © 1980 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.

Abstract

Relative complements and differences are investigated for several convergence structure lattices, especially the lattices of Kent convergence structures and the lattice of pretopologies. Convergence space properties preserved by relative complementation are studied. Mappings of some convergence structure lattices into related lattices of lattice homomorphisms are considered.