General Topology - Definition

Definition

A topology is a pair (X,Σ) consisting of a set X and a collection Σ of subsets of X, called open sets, satisfying the following three axioms:

  1. The union of open sets is an open set.
  2. The finite intersection of open sets is an open set.
  3. X and the empty set ∅ are open sets.

Read more about this topic:  General Topology

Famous quotes containing the word definition:

    The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.
    William James (1842–1910)

    I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.”
    Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)

    One definition of man is “an intelligence served by organs.”
    Ralph Waldo Emerson (1803–1882)