Indicate if
is a lattice. Justify.
Definition Let $(A,\preceq)$ be a ordered set. $(A,\preceq)$ is a lattice if between all pair of elements the supreme and the infimum must exist.
I think it is not a lattice since the atoms i.e. the $\color{red}{\text{red points}}$ do not have supreme because they have two maximum elements (in $\color{blue}{\text{blue}}$):
Am I correct?