Open Access
2007 The Propositional Theory of Closure
A. E. McCluskey, D. W. McIntyre, W. S. Watson
Experiment. Math. 16(4): 501-512 (2007).


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.


Download Citation

A. E. McCluskey. D. W. McIntyre. W. S. Watson. "The Propositional Theory of Closure." Experiment. Math. 16 (4) 501 - 512, 2007.


Published: 2007
First available in Project Euclid: 6 March 2008

zbMATH: 1138.54003
MathSciNet: MR2378489

Primary: 54A05
Secondary: 54D10 , 54F65 , 54G05

Keywords: closure operator , extremally disconnected space , formal system

Rights: Copyright © 2007 A K Peters, Ltd.

Vol.16 • No. 4 • 2007
Back to Top