Difference between revisions of "Subbasis"
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| − | A '''subbasis''' ''S'' for a topology on ''X'' is a collection of subsets of X whose union is ''X''. The '''topology generated by the subbasis ''S''''' is defined to be the collection ''T'' of all unions of finite intersections of elements in ''S''. | + | A '''subbasis''' ''S'' for a [[topology]] on ''X'' is a collection of subsets of X whose union is ''X''. The '''topology generated by the subbasis ''S''''' is defined to be the collection ''T'' of all unions of finite intersections of elements in ''S''. |
[[category:topology]] | [[category:topology]] | ||
Revision as of 23:37, November 2, 2007
A subbasis S for a topology on X is a collection of subsets of X whose union is X. The topology generated by the subbasis S is defined to be the collection T of all unions of finite intersections of elements in S.