Weak Relative Pseudo - Complements of Closure OperatorsRoberto
نویسندگان
چکیده
We deene the notion of weak relative pseudo-complement, and we show that, for an arbitrary lattice, the property of weak relative pseudo-complementation is strictly weaker than relative pseudo-complementation, but stronger than pseudo-complementation. Our main interest for this notion is in relation with the theory of closure operators. We prove that if a complete lattice L is completely inf-distributive with respect to chains, then every closure operator on L admits weak relative pseudo-complements with respect to continuous closure operators on L.
منابع مشابه
Weak Relative Pseudo-Complements of Closure Operators
We define the notion of weak relative pseudo-complement on meet semi-lattices, and we show that it is strictly weaker than relative pseudo-complementation, but stronger than pseudo-complementation. Our main result is that if a complete lattice L is meet-continuous, then every closure operator on L admits weak relative pseudo-complements with respect to continuous closure operators on L.
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