A normed space \(V\) is called Banach space if it is complete .

Examples Link to heading

• space of bounded functions \(l^\infty\)

Continuous Functions Link to heading

• space of bounded continuous functions \(\mathcal{C}^b\)
• space of continuous functions vanishing at infinity \(C_0\)
• Hölder Space \(\mathcal{C}^{k,\gamma}\)

Integrable Functions Link to heading

• Integrable functions \(L^p\)
• Sobolev space \(W^{k,p}\)