Let $H$ be the set of Hermitian matrices ordered by $P$ the cone of positive semi-definite matrices and $M,N\in int(P)$ ($int(P)$ is the interior of $P$) such that $M<N$ ($M\le N$ and $M\ne N$). Why the order-interval $[M, N]$ is compact?
2026-04-22 11:29:07.1776857347
Why an order interval in a finite dimensional Banach space is compact?
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