Editing Continuous linear extension (section)

{{Short description|Mathematical method in functional analysis}}
In [[functional analysis]], it is often convenient to define a [[linear transformation]] on a [[Complete space|complete]], [[normed vector space]] <math>X</math> by first defining a linear transformation <math>L</math> on a [[dense set|dense]] [[subset]] of <math>X</math> and then [[Continuous extension|continuously extending]] <math>L</math> to the whole space via the theorem below. The resulting extension remains [[Linear map|linear]] and [[Bounded operator|bounded]], and is thus [[continuous function|continuous]], which makes it a '''continuous [[Linear extension (linear algebra)|linear extension]]'''. 

This procedure is known as '''continuous linear extension'''.