Preorderable topologies and order-representability of topological spaces

doi:10.1016/j.topol.2009.01.018

Topology and its Applications

Volume 156, Issue 18, 1 December 2009, Pages 2971-2978

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Abstract

We furnish characterizations of topologies that coincide with the lower topology or with the order topology of some total preorder defined on a set. Leaning on these characterizations we introduce some applications to the study of continuous and semicontinuous order-representability properties of topological spaces.

MSC

primary

54F05

secondary

06A05

Keywords

Orderability properties on topological spaces

Topologies induced by a total preorder

Order-representability properties on topological spaces