A maximal chain approach to topology and order

R. Vainio

International Journal of Mathematics and Mathematical Sciences, 1988, vol. 11, 1-8

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.

Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:107468

DOI: 10.1155/S0161171288000547

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