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Isolated points and redundancy

P. Alirio J. PeñaJorge E. Vielma — 2011

Commentationes Mathematicae Universitatis Carolinae

We describe the isolated points of an arbitrary topological space ( X , τ ) . If the τ -specialization pre-order on X has enough maximal elements, then a point x X is an isolated point in ( X , τ ) if and only if x is both an isolated point in the subspaces of τ -kerneled points of X and in the τ -closure of { x } (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 Spec ( R ) of a (commutative...

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