Editing General topology (section)

===Basis for a topology===
{{Main|Basis (topology)}}
A '''base''' (or '''basis''') ''B'' for a [[topological space]] ''X'' with [[topological space|topology]] ''T'' is a collection of [[open set]]s in ''T'' such that every open set in ''T'' can be written as a union of elements of ''B''.<ref>{{cite book |last1=Merrifield |first1=Richard E. |last2=Simmons |first2=Howard E. |author-link2=Howard Ensign Simmons Jr. |title=Topological Methods in Chemistry |year=1989 |publisher=John Wiley & Sons |location=New York |isbn=0-471-83817-9 |url=https://archive.org/details/topologicalmetho00merr/page/16 |access-date=27 July 2012 |pages=[https://archive.org/details/topologicalmetho00merr/page/16 16] |quote='''Definition.''' A collection ''B'' of subsets of a topological space ''(X,T)'' is called a ''basis'' for ''T'' if every open set can be expressed as a union of members of ''B''. |url-access=registration }}</ref><ref>{{cite book |last=Armstrong |first=M. A. |title=Basic Topology |year=1983 |publisher=Springer |isbn=0-387-90839-0  |url=https://www.springer.com/mathematics/geometry/book/978-0-387-90839-7 |access-date=13 June 2013 |page=30 |quote=Suppose we have a topology on a set ''X'', and a collection <math>\beta</math> of open sets such that every open set is a union of members of <math>\beta</math>. Then <math>\beta</math> is called a ''base'' for the topology...}}</ref>  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 that generates that topology—and because many topologies are most easily defined in terms of a base that generates them.