Tietze extension theorem

Let X be a topological spaceMathworldPlanetmath. Then the following are equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath:

  1. 1.

    X is normal.

  2. 2.

    If A is a closed subset in X, and f:A[-1,1] is a continuous functionMathworldPlanetmathPlanetmath, 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].


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