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The propositional theory of closure. (English) Zbl 1138.54003

Authors’ summary: We study the simplest fragment of topological theory: those statements that can be expressed using one set variable, interior and closure operators, and inclusion. We introduce a formal system that is simple enough to be implemented on a computer and exhaustively studied and yet rich enough to be sound and complete for the fragment of theory under consideration. This fragment is rich enough to capture concepts such as regular open sets, extremal disconnectedness, partition topologies, and the nodec property.

MSC:

54A05 Topological spaces and generalizations (closure spaces, etc.)
54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
54F65 Topological characterizations of particular spaces
54G05 Extremally disconnected spaces, \(F\)-spaces, etc.
03B99 General logic
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