General Concepts
Traditionally, a topological space consists of a set of points, together with a system of open sets. These open sets with the operations of intersection and union form a lattice with certain properties. Pointless topology then studies lattices like these abstractly, without reference to any underlying set of points. Since some of the so-defined lattices do not arise from topological spaces, one may see the category of pointless topological spaces, also called locales, as an extension of the category of ordinary topological spaces.
Read more about this topic: Pointless Topology
Famous quotes containing the words general concepts, general and/or concepts:
“Without metaphor the handling of general concepts such as culture and civilization becomes impossible, and that of disease and disorder is the obvious one for the case in point. Is not crisis itself a concept we owe to Hippocrates? In the social and cultural domain no metaphor is more apt than the pathological one.”
—Johan Huizinga (1872–1945)
“A writer who writes, “I am alone” ... can be considered rather comical. It is comical for a man to recognize his solitude by addressing a reader and by using methods that prevent the individual from being alone. The word alone is just as general as the word bread. To pronounce it is to summon to oneself the presence of everything the word excludes.”
—Maurice Blanchot (b. 1907)
“Institutional psychiatry is a continuation of the Inquisition. All that has really changed is the vocabulary and the social style. The vocabulary conforms to the intellectual expectations of our age: it is a pseudo-medical jargon that parodies the concepts of science. The social style conforms to the political expectations of our age: it is a pseudo-liberal social movement that parodies the ideals of freedom and rationality.”
—Thomas Szasz (b. 1920)