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
The moor-hen guides upon the stream,
To silence the envy in my thought;
And turn towards my chamber, caught
In the cold snows of a dream.”
—William Butler Yeats (1865–1939)
“through the spaces of the dark
Midnight shakes the memory
As a madman shakes a dead geranium.”
—T.S. (Thomas Stearns)