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Normal Space

According to many authors (e.g., Kelley 1955, p. 112; Joshi 1983, p. 162; Willard 1970, p. 99) a normal space is a topological space in which for any two disjoint closed sets C,D there are two disjoint open sets U and V such that C subset= U and D subset= V.

Other authors (e.g., Cullen 1968, p. 118) define the notion differently, using separation axioms.

See also

Hilbert Cube, Tietze's Extension Theorem, Tychonoff Plank, Urysohn's Lemma

This entry contributed by Margherita Barile

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References

Cullen, H. F. "Normal Spaces. Completely Regular Spaces." §18 in Introduction to General Topology. Boston, MA: Heath, pp. 118-139, 1968.Joshi, K. D. Introduction to General Topology. New Delhi, India: Wiley, 1983.Kelley, J. L. General Topology. New York: Van Nostrand, 1955.Willard, S. "Normal Spaces." §15 in General Topology. Reading, MA: Addison-Wesley, pp. 99-108, 1970.

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Normal Space

Cite this as:

Barile, Margherita. "Normal Space." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/NormalSpace.html

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