Before revision:  It turns out that if the topological space X is quasi-compact and sequentially compact, then any element x\in X is R-dominated by an R-maximal element m\in X: xRm . In particular, since the (n-1)-dimensional simplex is a compact subset of the real n-dimensional vector space, then considering its members as portfolios consisting of n financial assets, we obtain the classical 1952 result of Harry Markowitz that any portfolio is dominated by an efficient portfolio.
After revision:  It turns out that if the topological space X is quasi-compact and sequentially compact, then any element x\in X is R-dominated by an R-maximal element of X . In particular, since the (n-1)-dimensional simplex is a compact subset of the real n-dimensional vector space, then considering its members as portfolios consisting of n financial assets, we obtain the classical 1952 result of Harry Markowitz that any portfolio is dominated by an efficient portfolio.