Description:
Mathematical discussions and pursuits.
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Help with proof in "Topology" 2nd ed. by Munkres
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On page 172, Theorem 27.1 Let X be a simply ordered set having the least upper bound property. In the order topology, each closed interval in X is compact. In step 1 given a < b, let A be a covering of [a,b] by sets open in [a,b] in the subspace topology Munkres first proves the following: If x is a... more »
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Pakistan, Argentina and Chile
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Dear Newsgroup: I have been taking about some kind of strategic balance in the Asia by expansion of Japan because of populace (over a billion) countries like China and India, with nuclear arms capabilities. We have noted that it was essential to have North Korea as a colony of Germany and Japan, with its nuclear technology transferred over to its... more »
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Multidimensional data visualization tool
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Hello All, We are pleased to announce the release of NovoSpark Visualizer 1.1. The new version contains many new features and improvements addressing the needs of our customers and making the tool even more convenient in their day-to-day work with multidimensional data. The fully-functional version of NovoSpark Visualizer can be downloaded... more »
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Germany and Japan
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Dear Newsgroup: The expansion of Japan in the area is essential to balance the forces between two large populated nations (over a billion) and with nuclear capabilities; these are countries of China and India. Thus I would like to suggest the following: 1-South Korea will be the colony of Japan 2-North Korea will be a colony of Germany and Japan (half each).... more »
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