International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 3, Pages 465-472
doi:10.1155/S0161171288000547
A maximal chain approach to topology and order
Department of mathematics, Åbo Akademi, Åbo SF-20500, Finland
Received 18 May 1987; Revised 26 August 1987
Copyright © 1988 R. Vainio. 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
On ordered sets (posets, lattices) we regard topologies (or, more general convergence
structures) which on any maximal chain of the ordered set induce its own interval topology. This construction generalizes several well-known intrinsic structures, and still contains enough to produce interesting results on for instance compactness and connectedness.
The “maximal chain compatibility” between topology (convergence structure) and order is preserved by formation of arbitrary products, at least in case the involved order structures are conditionally complete lattices.