TY - JOUR
AU - Caserta, Agata
AU - Giarlotta, Alfio
AU - Watson, Stephen
PY - 2006/10/01
Y2 - 2024/04/13
TI - On resolutions of linearly ordered spaces
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 7
IS - 2
SE -
DO - 10.4995/agt.2006.1925
UR - https://polipapers.upv.es/index.php/AGT/article/view/1925
SP - 211-231
AB - We define an extended notion of resolution of topologicalspaces, where the resolving maps are partial instead of total. To showthe usefulness of this notion, we give some examples and list severalproperties of resolutions by partial maps. In particular, we focus ourattention on order resolutions of linearly ordered sets. Let X be a setendowed 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 LOTSand ı : X â†’֒֒Y is an injective, order-preserving and open-in-the-rangefunction. We exhibit a canonical unification (Y, ı) of (X,, τ ) such thatY is an order resolution of a GO-space (X,, τ âˆ—), whose topology τ âˆ—refines τ . We prove that (Y, ı) is the unique minimum unification ofX. Further, we explicitly describe the canonical unification of an orderresolution.
ER -