A characterization of
normal spaces with respect to the definition given by Kelley (1955, p. 112) or Willard (1970, p. 99).
It states that the topological space is normal iff,
for all closed subsets of , every continuous function ,
denotes the real line with the Euclidean
topology, can be extended to a continuous function (Willard 1970, p. 103).
With respect to the alternative definition (Cullen 1968, p. 118), the statement is different: if
is a T4-space, for all closed
every continuous bounded function can be extended to a continuous bounded function .
(Cullen 1968, p. 127)
Another characterization of normality in terms of maps is
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References Cullen, H. F. Boston, MA: Heath, 1968. Introduction to General Topology. Joshi, K. D.
"The Tietze Characterization of Normality." §7.44 in New Delhi, India: Wiley, pp. 182-188, 1983. Introduction
to General Topology. Kelley,
J. L. New York: Van Nostrand, 1955. General
Topology. Willard, S. Reading, MA: Addison-Wesley, pp. 99-108, 1970. General
on Wolfram|Alpha Tietze's Extension Theorem
Cite this as:
Barile, Margherita. "Tietze's Extension Theorem." From --A Wolfram Web Resource, created by MathWorld Eric
W. Weisstein. https://mathworld.wolfram.com/TietzesExtensionTheorem.html