Math and science::Topology

# Finer and coarser topologies

We say that one topology $$\mathcal{T}$$ on $$X$$ is finer than another topology $$\mathcal{T}'$$ on $$X$$ iff [in words...]. $$\mathcal{T}'$$ is said to be coarser than $$\mathcal{T}$$.

Stronger and weaker are alternative terminology for finer and coarser.

$$\mathcal{T}$$ is strictly finer iff [...]

Symbolically,

• $$\mathcal{T}$$ is finer than $$\mathcal{T}'$$ ⟺ [...].
• $$\mathcal{T}$$ is strictly finer than $$\mathcal{T}'$$ ⟺ [...].