Base (topology)
In mathematics, a base (or basis) B for a topological space X with topology T is a collection of open sets in T such that every open set in T can be written as a union of elements of B. We say that the base generates the topology T. Bases are useful because many properties of topologies can be reduced to statements about a base generating that topology, and because many topologies are most easily defined in terms of a base which generates them.
Read more about Base (topology): Simple Properties of Bases, Objects Defined in Terms of Bases, Theorems, Base For The Closed Sets, Weight and Character
Famous quotes containing the word base:
“When a man speaks the truth in the spirit of truth, his eye is as clear as the heavens. When he has base ends, and speaks falsely, the eye is muddy and sometimes asquint.”
—Ralph Waldo Emerson (1803–1882)