Document Zbl 1161.46302

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Continuous convexity and canonical partial metrics in normed spaces. (English) Zbl 1161.46302

Bull. Belg. Math. Soc. - Simon Stevin 15, No. 3, 547-559 (2008).

Summary: The aim of this paper is to study the canonical partial metric associated to the norm of a normed space, whose related non-translation-invariant topology can be used to characterize the convexity properties of the original space. In order to do this, we define and characterize a new intermediate geometric property that we call continuous convexity which appears in a natural way in the context of the canonical partial metric topology.

MSC:

46B20	Geometry and structure of normed linear spaces
54E35	Metric spaces, metrizability

Keywords:

partial metric; normed space

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