Continuity in Separable Metrizable and Lindelöf Spaces
نویسنده
چکیده
Given a map T : X → X on a set X we examine under what conditions there is a separable metrizable or an hereditarily Lindelöf or a Lindelöf topology on X with respect to which T is a continuous map. For separable metrizable and hereditarily Lindelöf, it turns out that there is a such a topology precisely when the cardinality ofX is no greater than the cardinality of the continuum. We go onto prove that there is a Lindelöf topology on X with respect to which T is continuous, if either Tc + (X) = Tc +1(X) 6= ∅ or Tα(X) = ∅ for some α < c+, where Tα+1(X) = T ( Tα(X) ) and Tλ(X) = ⋂ α<λ T α(X) for any ordinals α and λ a limit.
منابع مشابه
Continuity in Separable Metrizable and Lindelöf Spaces
Given a map T : X → X on a set X we examine under what conditions there is a separable metrizable or an hereditarily Lindelöf or a Lindelöf topology on X with respect to which T is a continuous map. For separable metrizable and hereditarily Lindelöf, it turns out that there is such a topology precisely when the cardinality of X is no greater than c, the cardinality of the continuum. We go on to...
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