Maps

In mathematics, for sets $S,T$, a map from $S$ to $T$ is a relation $R$ from $S$ to $T$ such that for each $x\in S$, there exists a unique $y\in T$ such that $(x,y)\in R$.

We define $S$ as the domain of the map, and $T$ as the codomain of the map. We usually compactly express this with:

$$f:S\to T$$

i.e., $x\to$ whatever $x$ gets mapped to.

Maps have several properties:

• Image
• Surjectivity
• Injectivity
• Bijectivity

Broad categories of maps include:

• Linear transformation, commonly called linear maps
• Functions