Lower Density Topologies

Autor: Dragan Jankovic, T. R. Hamlett, D. A. Rose
Rok vydání: 1993
Předmět:
Zdroj: Annals of the New York Academy of Sciences. 704:309-321
ISSN: 1749-6632
0077-8923
DOI: 10.1111/j.1749-6632.1993.tb52533.x
Popis: By considering lower density operators and their induced topologies in a general setting, some results of S. Scheinberg and E. Ľazarow et al. are unified and generalized. It is also shown that every σ-finite complete measure space (X, M, m) has a lower density operator and that every such operator induces a topology making X a category measure space in the sense of J. C. Oxtoby, except that the measure need not be finite. One consequence is that category σ-finite measure spaces must have the countable chain condition. Also, for every topological space (X, |Gt), there is a lower density operator on the σ-field of sets having the property of Baire (relative to the σ-ideal of meager sets). Further, in both the “measure” and “category” contexts, all induced lower density topologies have simple form. Finally, it is shown that the deep. J-density operator on the σ-field of subsets of the real line having the property of Baire is not a lower density operator.
Databáze: OpenAIRE
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