Four Continuities on the Real Line
نویسندگان
چکیده
The two most commonly used topologies on R are the ordinary topology and the density topology. The ordinary topology is, of course, more widely known, and has the open intervals as its basic sets. The density topology, on the other hand, appears naturally in deeper studies of the structure of measurable sets. Its open sets are all measurable sets S ⊂ R which have the property that if x ∈ S, then x is a Lebesgue density point of S; i.e.,
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