Regular Space
المؤلف:
Bourbaki, N.
المصدر:
"Regular Spaces." §1.4 in Elements of Mathematics: General Topology. Berlin: Springer-Verlag
الجزء والصفحة:
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4-8-2021
3249
Regular Space
According to most authors (e.g., Kelley 1955, p. 113; McCarty 1967, p. 144; Willard 1970, p. 92) a regular space is a topological space in which every neighborhood of a point contains a closed neighborhood of the same point.
Another equivalent condition is the following: for every closed set 
and every point 
there are two disjoint open sets 
and 
such that 
and 
.
In other sources (e.g., Bourbaki 1989, p. 80; Cullen 1968, p. 113) regularity is defined differently, using separation axioms.
REFERENCES:
Bourbaki, N. "Regular Spaces." §1.4 in Elements of Mathematics: General Topology. Berlin: Springer-Verlag, pp. 80-81, 1989.
Cullen, H. F. "Regular Spaces." §17 in Introduction to General Topology. Boston, MA: Heath, pp. 113-118, 1968.
Kelley, J. L. General Topology. New York: Van Nostrand, 1955.
McCarty, G. "Regularity and 
-Spaces." In Topology, an Introduction. New York: McGraw-Hill, pp. 144-146, 1967.
Willard, S. "Regularity and Complete Regularity." §14 in General Topology. Reading, MA: Addison-Wesley, pp. 92-99, 1970.
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