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: Pointlessly
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)
“As a general rule, do not kick the shins of the opposite gentleman under the table, if personally unaquainted with him; your pleasantry is liable to be misunderstood—a circumstance at all times unpleasant.”
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“During our twenties...we act toward the new adulthood the way sociologists tell us new waves of immigrants acted on becoming Americans: we adopt the host culture’s values in an exaggerated and rigid fashion until we can rethink them and make them our own. Our idea of what adults are and what we’re supposed to be is composed of outdated childhood concepts brought forward.”
—Roger Gould (20th century)