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 and/or concepts:
“The first general store opened on the ‘Cold Saturday’ of the winter of 1833 ... Mrs. Mary Miller, daughter of the store’s promoter, recorded in a letter: ‘Chickens and birds fell dead from their roosts, cows ran bellowing through the streets’; but she failed to state what effect the freeze had on the gala occasion of the store opening.”
—Administration in the State of Sout, U.S. public relief program (1935-1943)
“Germany collapsed as a result of having engaged in a struggle for empire with the concepts of provincial politics.”
—Albert Camus (1913–1960)