Experimental Mathematics

The Propositional Theory of Closure

A. E. McCluskey, D. W. McIntyre, and W. S. Watson

Full-text: Open access


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.

Article information

Experiment. Math. Volume 16, Issue 4 (2007), 501-512.

First available in Project Euclid: 6 March 2008

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 54A05: Topological spaces and generalizations (closure spaces, etc.)
Secondary: 54D10: Lower separation axioms (T0-T3, etc.) 54F65: Topological characterizations of particular spaces 54G05: Extremally disconnected spaces, $F$-spaces, etc.

Closure operator formal system extremally disconnected space


McCluskey, A. E.; McIntyre, D. W.; Watson, W. S. The Propositional Theory of Closure. Experiment. Math. 16 (2007), no. 4, 501--512. http://projecteuclid.org/euclid.em/1204836518.

Export citation