Topologization of Power Set
Since any family of functions XY from Y to X might be topologized establishing the so-called function space, the same can be done with the power set 2S identified as {0,1}S. This particular type of function space is often called a hyperspace and the topology on the power set is referred to as hypertopology.
Read more about this topic: Power Set
Famous quotes containing the words power and/or set:
“First, there is the power of the Wind, constantly exerted over the globe.... Here is an almost incalculable power at our disposal, yet how trifling the use we make of it! It only serves to turn a few mills, blow a few vessels across the ocean, and a few trivial ends besides. What a poor compliment do we pay to our indefatigable and energetic servant!”
—Henry David Thoreau (1817–1862)
“I hate the whole race.... There is no believing a word they say—your professional poets, I mean—there never existed a more worthless set than Byron and his friends for example.”
—Arthur Wellesley, 1st Duke Wellington (1769–1852)