Vector space/Norm/Equivalent/Definition

Let ${\displaystyle {}V}$ be a ${\displaystyle {}{\mathbb {K} }}$-vector space. Two norms ${\displaystyle {}\Vert {-}\Vert _{1}}$ and ${\displaystyle {}\Vert {-}\Vert _{2}}$ are called equivalent, if they define the same topology, that is, the same open sets.