# Download Barrelledness in Topological and Ordered Vector Spaces by T. Husain, S.M. Khaleelulla PDF

By T. Husain, S.M. Khaleelulla

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Extra info for Barrelledness in Topological and Ordered Vector Spaces

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THE NONIUS SCALE In the 16th century, sea navigation still depended on mariner’s astrolabes and other relatively primitive instruments for measuring astronomical altitudes. The precision of these instruments was greatly limited by the graduated scale they used, which was normally based on a minimum unit of one degree and could be subdivided into half-degrees but not into smaller units, as the measurement marks engraved in the metal instruments had to have a certain width, and began to become indistinguishable if placed too close together.

Here, for example, if we want to introduce number 1, we’d have four options. Some people choose one cell tentatively, and then scratch it, if necessary (in computation we call this a “backtracking”). The puzzle I am about to describe has an intriguing name, and one you’ve surely heard about. You can write it as “sudoku” or “su doku”, as you prefer. It comes from the Japanese: “su” means “number” or “counting”, and “doku” means “single” or “unique”. In order to N. 1007/978-3-642-04833-3_8, C Springer-Verlag Berlin Heidelberg 2010 31 32 FIGURING IT OUT complete this puzzle, you have to insert numbers into empty boxes.

The short answer is, not really, though the reality, while less frightening, is much more fascinating. S. Department of Defense in the 1970s and 1980s, but which is accessible to the public. The system consists of three elements: a network of satellites, terrestrial control stations, and users operating GPS receivers. The network of satellites comprises 24 devices positioned across six diﬀerent orbital planes in such a way that, no matter where you are in the world, it is always possible to receive signals from at least four of the twenty-four satellites at any given time.

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