Abstract Let F be an ordered topological vector space (over $$\mathbb {R}$$ R ) whose positive cone $$F_+$$ F + is weakly closed, and let $$E \subseteq F$$ E ⊆ a subspace. We prove that the set of...

A major breakthrough in the theory of topological algorithms occurred in 1992 when Hyam Rubinstein introduced the idea of an almost normal surface. We explain how almost normal surfaces emerged naturally from the study of geodesics and minimal surfaces. Patterns of stable and unstable geodesics can be used to characterize the 2-sphere among surfaces, and similar patterns of normal and almost no...