A topological space \(X\) is called completely Hausdorff if for every pair of distinct points \(a,b\in X\) there are open sets \(U,V\subseteq X\) such that \[a\in U,\qquad b\in V,\qquad \overline U\cap\overline V=\varnothing.\] Show that the product of two completely Hausdorff spaces is completely Hausdorff.
Products of completely Hausdorff spaces are completely Hausdorff
P-SQUAL2-03
- Area
- Topology
- Status
- draft