Changes

If ''B'' satisfy the above 2 conditions, then the '''topology ''T'' generated by ''B''''' is the collection of subsets ''U'' of ''X'' such that for each ''x'' in ''U'', there is a basis element ''V'' in ''B'' such that ''x'' is in ''V'' and ''V'' is a subset of ''U''.

If ''B'' satisfy the above 2 conditions, then the '''topology ''T'' generated by ''B''''' is the collection of subsets ''U'' of ''X'' such that for each ''x'' in ''U'', there is a basis element ''V'' in ''B'' such that ''x'' is in ''V'' and ''V'' is a subset of ''U''.

When the topological space is a [[vector|vector space]] V, the basis generates V under the operations of [[addition]] and [[scalar]] multiplication.

When the topological space is a [[vector|vector space]] V, the basis generates V under the [[continuous]] operations of [[addition]] and [[scalar]] multiplication. The [[dimension]] of V is given by the number of elements in the basis, up to intersection and multiplicity.

[[category:topology]][[category:algebra]]

[[category:topology]][[category:algebra]]