How are normal and T4 spaces defined in books?
A recent discussion on PlanetMath has led me to consider how various sources 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 on the question of how to define it. I am not giving precise references at this time, and may choose to never do that. I think the abbreviated form 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.
|Alexandroff and Hopf||T1+S||T1+S||68||1935|
|Hocking and Young||T1+S||T1+S||41||1961|
|Steen and Seebach||T1+S||S||12||1970|
|Title||How are normal and T4 spaces defined in books?|
|Date of creation||2013-03-22 17:09:12|
|Last modified on||2013-03-22 17:09:12|
|Last modified by||Mathprof (13753)|