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Many properties coincide: the dcpo is, equivalently, algebraic, continuous, meet-continuous, atomistic, quasi-algebraic or quasi-continuous, if and only if the C*-algebra is scattered. For C*-algebras with enough projections, these properties are equivalent to finite-dimensionality. Approximately finite-dimensional elements of the dcpo correspond to Boolean subalgebras of the projections of the C*-algebra. Scattered C*-algebras are finitedimensional if and only if their dcpo is Lawson-scattered. General C*-algebras are finite-dimensional if and only if their dcpo is order-scattered.<\/jats:p>","DOI":"10.1017\/s0960129518000464","type":"journal-article","created":{"date-parts":[[2019,3,21]],"date-time":"2019-03-21T08:47:03Z","timestamp":1553158023000},"page":"972-1006","source":"Crossref","is-referenced-by-count":0,"title":["Domains of commutative C*-subalgebras"],"prefix":"10.1017","volume":"29","author":[{"given":"Chris","family":"Heunen","sequence":"first","affiliation":[]},{"given":"Bert","family":"Lindenhovius","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2019,3,21]]},"reference":[{"key":"S0960129518000464_ref42","volume-title":"Banach Spaces of Continuous Functions, Volume 1","author":"Semadeni","year":"1971"},{"key":"S0960129518000464_ref40","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(71)90105-0"},{"key":"S0960129518000464_ref4","unstructured":"Bice, T. and Koszmider, P. (2017). 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