# Illustration Elements of a topology

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The elements of a topology $$\class{blue}{\mathcal{T}}$$ of a topological space $$(\mathbb{X}, \class{blue}{\mathcal{T}})$$ must satisfy three properties:

1. The empty set $$\emptyset$$ and the whole set $$X$$ are both inside $$\mathcal{T}$$.
2. The union of any (even infinitely many) elements $$\mathbb{T}_i$$ of $$\class{blue}{\mathcal{T}}$$ is also an element of $$\class{blue}{\mathcal{T}}$$.
3. The intersection of finitely many elements $$\mathbb{T}_i$$ of $$\class{blue}{\mathcal{T}}$$ is also an element of $$\class{blue}{\mathcal{T}}$$.