Question #115196
Give an example of a regular space that is not normal
1
Expert's answer
2020-05-13T18:23:42-0400

An example of a regular space that is not normal is the Sorgenfrey plane - Rl×Rl\mathbb{R}_l\times\mathbb{R}_l

 It is regular because it is the Cartesian product of regular spaces. It is not normal because any subset 

A of Δ={x×(x)xR}-\Delta=\{x\times(-x)|x\in\mathbb{R}\}  is a closed subspace of Rl2\mathbb{R}_l^2 and it can be shown that there do not exist disjoint open sets about A and ΔA-\Delta \setminus A in Rl2\mathbb{R}_l^2


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