Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
MATHEMATICA
Vol. 58, No. 1, pp. 121-125 (2001)

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A Counterexample to A Result Concerning Closure Operators

Francesco Ranzato

Dipartimento di Matematica Pura ed Applicata, Università di Padova
Via Belzoni 7, 35131 Padova -- ITALY E-mail: franz@math.unipd.it
URL: http://www.math.unipd.it/ franz

Abstract: In 1960, José Morgado gave a necessary and sufficient condition on a poset $P$ in order that closure operators on $P$, ordered pointwise, form a complete lattice. This result was based on a notion of relative quasi-infimum in posets. This note shows that Morgado's result is flawed.

Keywords: Closure operator; Relative quasi-infimum.

Classification (MSC2000): 06A15 (06A23, 06A06).

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Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.

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