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.
| Source | Normal | T4 | Page | Year |
|---|---|---|---|---|
| Alexandroff and Hopf | T1+S | T1+S | 68 | 1935 |
| Wilder | S | ? | 49 | 1949 |
| Kelley | S | T1+S | 112 | 1955 |
| Hocking and Young | T1+S | T1+S | 41 | 1961 |
| Pervin | S | T1+S | 88 | 1964 |
| Gaal | T1+S | S | 87 | 1964 |
| Lipschutz | S | T1+S | 141 | 1965 |
| Husain | T1+S | S | 7 | 1966 |
| Dugundji | T2+S | T2+S | 144 | 1966 |
| Gemignani | T1+S | S | 102 | 1967 |
| Willard | S | T1+S | 99 | 1970 |
| Steen and Seebach | T1+S | S | 12 | 1970 |
| Maunder | S | - | 15 | 1970 |
| Munkres | T1+S | - | 195 | 1975 |
| Morris | S | T2+S | 121 | 1988 |
| Repovš | T1+S | S | 6 | 1998 |
| Stroppel | T2+S | S | 6 | 2006 |
| Title | How are normal and T4 spaces defined in books? |
|---|---|
| Canonical name | HowAreNormalAndT4SpacesDefinedInBooks |
| Date of creation | 2013-03-22 17:09:12 |
| Last modified on | 2013-03-22 17:09:12 |
| Owner | Mathprof (13753) |
| Last modified by | Mathprof (13753) |
| Numerical id | 12 |
| Author | Mathprof (13753) |
| Entry type | Topic |
| Classification | msc 54D15 |
| Related topic | UrysohnsLemma |
| Related topic | T4Space |