Optimal Quasi-metrics in a given Pointwise Equivalence Class Do Not Always Exist
نویسندگان
چکیده
In this paper we provide an answer to a question found in [3], namely when given a quasi-metric ρ, if one examines all quasi-metrics which are pointwise equivalent to ρ, does there exist one which is most like an ultrametric (or, equivalently, exhibits an optimal amount of Hölder regularity)? The answer, in general, is negative, which we demonstrate by constructing a suitable Rolewicz–Orlicz space. 2010 Mathematics Subject Classification: Primary: 46E30, 52A07; Secondary: 46A16, 46A80, 54E35, 54E50.
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تاریخ انتشار 2015