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:
“There is a Restlessness springing from the consciousness of power not fully utilized, which must be present wherever there is unused power of whatever kind. This is the restlessness of the germ within the seed, struggling upward and downward towards its proper life. ... it is a striving full of pain, the cutting of tender flesh by the fetters of the captive as he struggles against their pitilessness.”
—Anna C. Brackett (1836–1911)
“With all her masculine vigour and glory, Greece fell, gradually atrophied, because one half of her had been, of set purpose, intellectually and politically paralyzed.”
—Tennessee Claflin (1846–1923)