Box Topology - Definition

Definition

Given such that

or the (possibly infinite) Cartesian product of the topological spaces, indexed by, the box topology on is generated by the base

The name box comes from the case of Rn, the basis sets look like boxes or unions thereof.

Read more about this topic:  Box Topology

Famous quotes containing the word definition:

    Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.
    Walter Pater (1839–1894)

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

    It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.”
    Jane Adams (20th century)