There exist normal topological spaces $(X,\tau_X)$ and $(Y,\tau_Y)$ such that the product space $X \times Y$, equipped with the [product topology](/page/Product%20Topology), is not a [normal topological space](/page/Normal%20Topological%20Space).
Knowledge Status
Analysis
Discussion
The product of two normal topological spaces need not be normal, showing normality is not preserved by products.