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Topologies generated by ideals

Carlos Uzcátegui (2006)

Commentationes Mathematicae Universitatis Carolinae

A topological space X is said to be generated by an ideal if for all A X and all x A ¯ there is E A in such that x E ¯ , and is said to be weakly generated by if whenever a subset A of X contains E ¯ for every E A with E , then A itself is closed. An important class of examples are the so called weakly discretely generated spaces (which include sequential, scattered and compact Hausdorff spaces). Another paradigmatic example is the class of Alexandroff spaces which corresponds to spaces generated by finite sets....

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