Balls in Normed Vector Spaces
Any normed vector space V with norm |·| is also a metric space, with the metric d(x, y) = |x − y|. In such spaces, every ball Br(p) is a copy of the unit ball B1(0), scaled by r and translated by p.
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Famous quotes containing the words balls and/or spaces:
“look the spangles
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—E.E. (Edward Estlin)
“Though there were numerous vessels at this great distance in the horizon on every side, yet the vast spaces between them, like the spaces between the stars,—far as they were distant from us, so were they from one another,—nay, some were twice as far from each other as from us,—impressed us with a sense of the immensity of the ocean, the “unfruitful ocean,” as it has been called, and we could see what proportion man and his works bear to the globe.”
—Henry David Thoreau (1817–1862)