Functional equations in total negation

Citation
Tbm. Mcmaster et Cr. Turner, Functional equations in total negation, J AUS MAT A, 68, 2000, pp. 334-339
Citations number
13
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS
ISSN journal
02636115 → ACNP
Volume
68
Year of publication
2000
Part
3
Pages
334 - 339
Database
ISI
SICI code
0263-6115(200006)68:<334:FEITN>2.0.ZU;2-S
Abstract
It is known that the only topological invariants P for which anti(P) = anti (2)(P), anti() denoting Bankston's total negation operator, are those which are determined purely by the cardinality of the underlying point-set. We e xamine equations of the form anti(n)(P) = anti(n)(not P), reaching similar conclusions for n less than or equal to 2 but weaker ones for n greater tha n or equal to 3. A corresponding investigation for total negation within a constraint is initiated. 2000 Mathematics subject classification: 54A25, 54 B05, 54D99.