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:
“Then must you speak
Of one the lov’d not wisely but too well;
Of one not easily jealous, but, being wrought,
Perplex’d in the extreme; of one whose hand,
Like the base Indian, threw a pearl away
Richer than all his tribe;”
—William Shakespeare (1564–1616)