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Line 6:
Line 6: − − 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.
deleted confusing and inappropriate comparison to vector space bases
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''.
[[category:topology]][[category:linear algebra]]
[[category:topology]][[category:linear algebra]]