Download Almost-periodic functions in abstract spaces by S. Zaidman PDF

By S. Zaidman

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E ......... .. 10 (Continuity of Distance from One Straight Line to Another). The distance function that assigns to each point in a given straight line the distance from it to another given straight line is continuous. Hint: Though not very difficult to obtain, the proof is a bit subtle. 11 (Divergence of Two Intersecting Straight Lines). If two straight lines intersect, then the distance from a point in one of the straight lines to the other increases without upper bounds as the point moves away from the intersection point of the two straight lines towards either end of the first straight line.

We shall see that an isometry of a hyperbolic plane resembles that of a Euclidean plane in many aspects: in both cases it is generated by three or fewer reflections in straight lines, and the differences lie in the different natures of two straight lines in respective planes. For detailed expositions of structures of isometries of the Euclidean plane, see Barker-Howe [1] or Martin [18]. 1. Isometries and reflections in straight lines We begin with the self-explaining definition of an isometry of the plane.

1 2 . . . . . . ... ........ ................................................................................................................................................................................ . .... P1 Fig. 18. 11.

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