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:
“... whilst you are proclaiming peace and good will to men, Emancipating all Nations, you insist upon retaining absolute power over wives. But you must remember that Arbitrary power is like most other things which are very hard, very liable to be broken—and notwithstanding all your wise Laws and Maxims we have it in our power not only to free ourselves but to subdue our Masters, and without violence throw both your natural and legal authority at our feet ...”
—Abigail Adams (1744–1818)
“One might get the impression that I recommend a new methodology which replaces induction by counterinduction and uses a multiplicity of theories, metaphysical views, fairy tales, instead of the customary pair theory/observation. This impression would certainly be mistaken. My intention is not to replace one set of general rules by another such set: my intention is rather to convince the reader that all methodologies, even the most obvious ones, have their limits.”
—Paul Feyerabend (1924–1994)