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Essential P-Spaces: A Generalization Of Door Spaces, Emad Abu Osba, Melvin Henriksen

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An element f of a commutative ring A with identity element is called a von Neumann regular element if there is a g in A such that f²g=f. A point p of a (Tychonoff) space X is called a P-point if each f in the ring C(X) of continuous real-valued functions is constant on a neighborhood of p. It is well-known that the ring C(X) is von Neumann regular ring iff each of its elements is a von Neumann regular element; in which case X is called a P-space. If all but at most one point of X …