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We define an extended notion of resolution of topological spaces, where the resolving maps are partial instead of total. To show the usefulness of this notion, we give some examples and list several properties of resolutions by partial maps. In particular, we focus our attention on order resolutions of linearly ordered sets. Let X be a set endowed with a Hausdorff topology τ and a (not necessarily related) linear order . A unification of X is a pair (Y, ı), where Y is a LOTS and ı : X ֒→ Y isdoi:10.4995/agt.2006.1925 fatcat:k2c4uugapvhxhckdo4mqbsuzhe