#bijective transformations

We say that: “oh I love that Baldur Gate, let’s crack out an isometric.” Or, “oh, digging this Final Fantasy Tactics stuff, let’s do that sideways angle thing.” But what does that mean? Let’s break it down mathematical. T:(X,∥⋅∥X)→(Y,∥⋅∥Y) is a isometric isomorphism if it is a linear isomorphism, and it is an isometry, that is ∥T(x)∥Y=∥x∥X∀x∈X; T:(X,∥⋅∥X)→(Y,∥⋅∥Y) is a topological…