Order embeddings of matrix intervals
Michiya Mori (Tokyo)
In this talk, we consider order isomorphisms between two subsets of the partially ordered set of $n\times n$ hermitian matrices, where $n$ is an integer with $2\leq n<\infty$. We explain that, if one of the subsets is open, then the other is also open and the order isomorphism is a homeomorphism. We also reveal the general form of order isomorphisms when one of the two subsets is an interval with nonempty interior.