Essential -spaces: a generalization of door spaces
Emad Abu Osba, Melvin Henriksen (2004)
Commentationes Mathematicae Universitatis Carolinae
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An element of a commutative ring with identity element is called a if there is a in such that . A point of a (Tychonoff) space is called a - if each in the ring of continuous real-valued functions is constant on a neighborhood of . It is well-known that the ring is von Neumann regular ring iff each of its elements is a von Neumann regular element; in which case is called a -. If all but at most one point of is a -point, then is called an . In earlier work...