Projective limits of probability spaces

Projective limits of topological vector spaces

Projective embedding of projective spaces

In this paper, embeddings φ : M → P from a linear space (M,M) in a projective space (P,L) are studied. We give examples for dimM > dimP and show under which conditions equality holds. More precisely, we introduce properties (G) (for a line L ∈ L and for a plane E ⊂ M it holds that |L ∩ φ(M)| 6 = 1) and (E) (φ(E) = φ(E) ∩ φ(M), whereby φ(E) denotes the by φ(E) generated subspace of P ). If (G) a...

Biquaternions Lie Algebra and Complex-Projective Spaces

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Affine Spaces within Projective Spaces

We endow the set of complements of a fixed subspace of a projective space with the structure of an affine space, and show that certain lines of such an affine space are affine reguli or cones over affine reguli. Moreover, we apply our concepts to the problem of describing dual spreads. We do not assume that the projective space is finitedimensional or pappian. Mathematics Subject Classification...

Metrizations of Projective Spaces

A two-dimensional G-space,1 in which the geodesic through two distinct points is unique, is either homeomorphic to the plane £2 and all geodesies are isometric to a straight line, or it is homeomorphic to the projective plane P2 and all geodesies are isometric to the same circle, see [l, §§10 and 31 ]. Two problems arise in either case: (1) To determine the systems of curves (in E2 or P2) which...