SkipCaptcha
1,279
edits
Changes
Jump to navigation
Jump to search
mLine 1:
Line 1: + + + + + + + + Line 7:
Line 15: − +
Fixed broken link
''Basis is a [[mathematics]] term.''
''Basis is a [[mathematics]] term.''
== Linear algebra ==
In [[linear algebra]], a basis is a set of [[linear independence|linearly independent]] vectors that [[spans]] a vector space ''V''. Any vector in the vector space can then be written as a linear combination of the basis.
This usage of the term is similar to its common usage: a basis is the foundation for what is needed.
== Topology ==
A '''basis''' ''B'' for a [[topology]] ''T'' on a set ''X'' is a collection of subsets of ''X'' (called '''basis elements''') such that
A '''basis''' ''B'' for a [[topology]] ''T'' on a set ''X'' is a collection of subsets of ''X'' (called '''basis elements''') such that
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]]