How are normal and T4 spaces defined in books?

A recent discussion on PlanetMath has led me to consider how varioussources define normal and T4 spaces. I limited myself to books, mostly textbooks.No articles were consulted.As will be seen from the table below, there is no agreement onthe question of how to define it. I am not giving precise referencesat this time, and may choose to never do that. I think the abbreviatedform may be sufficient for those that seek to check what I have done.If you want to add something to the table, file a correction.S refers to the condition that closed sets can be separated by open sets.The condition S is due to Tietze, according to Alexandroff and Hopf.Of course, T1 + S is the same as T2 +S.

单词	HowAreNormalAndT4SpacesDefinedInBooks
释义	How are normal and T4 spaces defined in books? A recent discussion on PlanetMath has led me to consider how varioussources define normal and T4 spaces. I limited myself to books, mostly textbooks.No articles were consulted.As will be seen from the table below, there is no agreement onthe question of how to define it. I am not giving precise referencesat this time, and may choose to never do that. I think the abbreviatedform may be sufficient for those that seek to check what I have done.If you want to add something to the table, file a correction.S refers to the condition that closed sets can be separated by open sets.The condition S is due to Tietze, according to Alexandroff and Hopf.Of course, T1 + S is the same as T2 +S.
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