Tietze extension theorem
Let X be a topological space. Then the following are equivalent
:
-
1.
X is normal.
-
2.
If A is a closed subset in X, and f:A→[-1,1] is a continuous function
, then f has a continuous to all of X. (In other words, there is a continuous function f∗:X→[-1,1] such that f and f∗ coincide on A.)
Remark: If X and A are as above, and f:A→(-1,1) is a continuous function, then f has a continuous to all of X.
The present result can be found in [1].
References
-
1
A. Mukherjea, K. Pothoven,
Real and Functional analysis
, Plenum press, 1978.
Title | Tietze extension theorem |
---|---|
Canonical name | TietzeExtensionTheorem |
Date of creation | 2013-03-22 13:35:30 |
Last modified on | 2013-03-22 13:35:30 |
Owner | matte (1858) |
Last modified by | matte (1858) |
Numerical id | 5 |
Author | matte (1858) |
Entry type | Theorem |
Classification | msc 54D15 |
Related topic | ApplicationsOfUrysohnsLemmaToLocallyCompactHausdorffSpaces |