Experimental Mathematics

The Propositional Theory of Closure

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

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 6 March 2008

Permanent link to this document
http://projecteuclid.org/euclid.em/1204836518

Mathematical Reviews number (MathSciNet)
MR2378489

Zentralblatt MATH identifier
1138.54003

Subjects
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.

Keywords
Closure operator formal system extremally disconnected space

Citation

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


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