M. H. Stone, "Algebraic characterizations of special Boolean rings", Fundamenta Mathematicae, 29(1937), pp. 223-302. Home/Search Document Not in Database Summary Related Articles Check |
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Modal Definability in Topology - Gabelaia (2001) (1 citation) (Correct)
....the following definition: Definition 1.3.2 The topological space is extremally disconnected if any of the following two equivalent conditions hold: 14 1. The closure of any open is open. 2. The closures of any two disjoint opens are disjoint. Extremally disconnected spaces were defined in [Stone 1937] and have been around in general topology ever since. As it appears, 2) characterizes the class of extremally disconnected topological spaces. This statement seems to be known to scholars working in the field. However we could not find the exact reference who first established it. Here is the ....
M. H. Stone, "Algebraic characterizations of special Boolean rings", Fundamenta Mathematicae, 29(1937), pp. 223-302.
The Lattice of Topological Domains: An Example of Mizar Development - Karno (Correct)
....of all domains of a given topological space is Boolean has been formulated. To present that one we first recall a definition of a class of topological spaces which is important here. A topological space X is called extremally disconnected if for every open subset A of X the closure A is open in X [20] (comp. 14] 8] In [11] the following characterization has been obtained. The lattice of all domains of a topological space X is modular if and only if X is extremally disconnected. Moreover, for every extremally disconnected space the lattice of all its domains coincide with both the lattice ....
M. H. Stone, Algebraic characterizations of special Boolean rings, Fundamenta Math., 29 (1937), 223--303.
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