# Subspace topology

In topology and related areas of mathematics, a **subspace** of a topological space *X* is a subset *S* of *X* which is equipped with a topology induced from that of *X* called the **subspace topology** (or the **relative topology**, or the **induced topology**, or the **trace topology**).

If a topological space having some topological property implies its subspaces have that property, then we say the property is **hereditary**. If only closed subspaces must share the property we call it **weakly hereditary**.