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Complete lattice ?
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Tsakanikas Nickos
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Complete lattice ?
Let \( \displaystyle C \left( \left[ 0,1 \right] \right) \) be the set of continuous real-valued functions on \( \left[ 0,1 \right] \) and define \( \; \displaystyle f \geq g \; \) if \( \displaystyle f(x) \geq g(x) \, , \, \forall x \in \left[ 0,1 \right] \; \). Show that \( \left( \displaystyle C \left( \left[ 0,1 \right] \right) \, , \, \geq \right) \) is a lattice. Is this lattice complete?