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- W272880212 abstract "Publisher Summary This chapter discusses the theory of parallels with applications to closed geodesics. The theory of parallels used to be the foundations of geometry, but the interest in it ceased almost entirely after the discovery of hyperbolic geometry, except for some isolated investigations as those of Dehn on the relations of the angle sum in a triangle to parallels in non-Archimedean geometries. A second topic that has failed to attract attention in the foundations of geometry is spaces with nonsymmetric distances. Whereas p qv → 0 is a natural condition preventing two distinct topologies, there are interesting geometries not satisfying p qv → ∞, in particular Funk's so-called Geometrie der spezifischen Masbestimmung." @default.
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- W272880212 date "1962-01-01" @default.
- W272880212 modified "2023-09-27" @default.
- W272880212 title "THE THEORY OF PARALLELS WITH APPLICATIONS TO CLOSED GEODESICS" @default.
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- W272880212 doi "https://doi.org/10.1016/b978-0-08-009610-0.50006-1" @default.
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