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## Complete lattice ?

Linear Algebra, Algebraic structures (Groups, Rings, Modules, etc), Galois theory, Homological Algebra
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?