Isolated points and redundancy
We describe the isolated points of an arbitrary topological space . If the -specialization pre-order on has enough maximal elements, then a point is an isolated point in if and only if is both an isolated point in the subspaces of -kerneled points of and in the -closure of (a special case of this result is proved in Mehrvarz A.A., Samei K., , J. Sci. Islam. Repub. Iran (1999), no. 3, 193–196). This result is applied to an arbitrary subspace of the prime spectrum of a (commutative...