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Isolated points and redundancy

P. Alirio J. Peña, Jorge 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., On commutative Gelfand rings, J. Sci. Islam. Repub. Iran 10 (1999), no. 3, 193–196). This result is applied to an arbitrary subspace of the prime...

Iterative differentiations in rings of unequal characteristic

Marilena Crupi, Gaetana Restuccia (2001)

Bollettino dell'Unione Matematica Italiana

Sia R un anello di caratteristica diseguale. Si stabiliscono formule generali per gli endomorfismi di una differenziazione F a o F c -iterativa di R , con c non zerodivisore di R. Tali formule sono note nel caso della caratteristica eguale.

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