caa a22 4500 445813830 CHVBK 20180317145219.0 cr unu---uuuuu 170323e20111101xx s 000 0 eng 10.1007/s11083-010-9193-x doi (NATIONALLICENCE)springer-10.1007/s11083-010-9193-x Order-Compactifications of Totally Ordered Spaces: Revisited [Elektronische Daten] [Guram Bezhanishvili, Patrick Morandi] Order-compactifications of totally ordered spaces were described by Blatter (J Approx Theory 13:56-65, 1975) and by Kent and Richmond (J Math Math Sci 11(4):683-694, 1988). Their results generalize a similar characterization of order-compactifications of linearly ordered spaces, obtained independently by Fedorčuk (Soviet Math Dokl 7:1011-1014, 1966; Sib Math J 10:124-132, 1969) and Kaufman (Colloq Math 17:35-39, 1967). In this note we give a simple characterization of the topology of a totally ordered space, as well as give a new simplified proof of the main results of Blatter (J Approx Theory 13:56-65, 1975) and Kent and Richmond (J Math Math Sci 11(4):683-694, 1988). Our main tool will be an order-topological modification of the Dedekind-MacNeille completion. In addition, for a zero-dimensional totally ordered space X, we determine which order-compactifications of X are Priestley order-compactifications. Springer Science+Business Media B.V., 2011 Ordered topological space nationallicence Order-compactification nationallicence Totally ordered space nationallicence Interval topology nationallicence Linearly ordered space nationallicence Dedekind-MacNeille completion nationallicence Bezhanishvili Guram Department of Mathematical Sciences, New Mexico State University, 88003-8001, Las Cruces, NM, USA aut Morandi Patrick Department of Mathematical Sciences, New Mexico State University, 88003-8001, Las Cruces, NM, USA aut Order Springer Netherlands 28/3(2011-11-01), 577-592 0167-8094 28:3<577 2011 28 11083 https://doi.org/10.1007/s11083-010-9193-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11083-010-9193-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bezhanishvili Guram Department of Mathematical Sciences, New Mexico State University, 88003-8001, Las Cruces, NM, USA aut NATIONALLICENCE 700 1- Morandi Patrick Department of Mathematical Sciences, New Mexico State University, 88003-8001, Las Cruces, NM, USA aut NATIONALLICENCE 773 0- Order Springer Netherlands 28/3(2011-11-01), 577-592 0167-8094 28:3<577 2011 28 11083 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer