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:
“I count those feathered balls of soot
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To silence the envy in my thought;
And turn towards my chamber, caught
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—William Butler Yeats (1865–1939)
“In any case, raw aggression is thought to be the peculiar province of men, as nurturing is the peculiar province of women.... The psychologist Erik Erikson discovered that, while little girls playing with blocks generally create pleasant interior spaces and attractive entrances, little boys are inclined to pile up the blocks as high as they can and then watch them fall down: “the contemplation of ruins,” Erikson observes, “is a masculine specialty.””
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