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Functional equations in total negation

Part of: Basic constructions Fairly general properties Generalities

Published online by Cambridge University Press:  09 April 2009

T. B. M. McMaster  and
C. R. Turner
T. B. M. McMaster
Affiliation:
Pure Mathematics Department Queen's UniversityBelfast BT7 1NN NorthernIreland e-mail: [email protected]
C. R. Turner
Affiliation:
School of Electrical and Mechanical Engineering University of Ulster at JordanstownNorthernIreland e-mail: [email protected]
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Abstract

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It is known that the only topological invariants P for which anti(P) = anti2 (P), anti( ) denoting Bankston's total negation operator, are those which are determined purely by the cardinality of the underlying point-set. We examine equations of the form antin (P) = antin (not P), reaching similar conclusions for n ≤ 2 but weaker ones for n > 3. A corresponding investigation for total negation within a constraint is initiated.

MSC classification

Secondary: 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets) 54B05: Subspaces 54D99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 68 , Issue 3 , June 2000 , pp. 334 - 339
Copyright
Copyright © Australian Mathematical Society 2000

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