Editing Infinite-dimensional holomorphy (section)

===Locally bounded holomorphy===
A function ''f'' : (''U'' ⊂ ''X'') → ''Y'' is said to be [[locally bounded]] if each point of ''U'' has a neighborhood whose image under ''f'' is bounded in ''Y''.  If, in addition, ''f'' is Gateaux holomorphic on ''U'', then ''f'' is '''locally bounded holomorphic'''.  In this case, we write ''f'' ∈ H<sub>LB</sub>(''U'',''Y'').
<!-- to be continued by User:Silly Rabit, I guess -->