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New page: A '''basis''' ''B'' for a topology ''T'' on a set ''X'' is a collection of subsets of ''X'' (called '''basis elements''') such that #each ''x'' in ''X'', is in at least one basis element. ...
A '''basis''' ''B'' for a topology ''T'' on a set ''X'' is a collection of subsets of ''X'' (called '''basis elements''') such that
#each ''x'' in ''X'', is in at least one basis element.
#if x is in the intersection of 2 basis elements ''B<sub>1</sub>'' and ''B<sub>2</sub>'', then it is in some basis element ''B<sub>3</sub>'', where ''B<sub>3</sub>'' is a subset of ''B<sub>1</sub> ∩ B<sub>2</sub>''.
[[category:topology]]
#each ''x'' in ''X'', is in at least one basis element.
#if x is in the intersection of 2 basis elements ''B<sub>1</sub>'' and ''B<sub>2</sub>'', then it is in some basis element ''B<sub>3</sub>'', where ''B<sub>3</sub>'' is a subset of ''B<sub>1</sub> ∩ B<sub>2</sub>''.
[[category:topology]]