Abstract. In this paper we introduce the notion of canonical partial metric associated to a norm to study geometric properties of normed spaces. In particular, we characterize strict convexity and uniform convexity of normed spaces in terms of the canonical partial metric defined by its norm. We prove that these geometric properties can be considered, in this sense, as topological properties that appear when we compare the natural metric topology of the space with the non translation invariant topology induced by the canonical partial metric in the normed space.2000 AMS Classification: 54E35, 46B04.

Addictions are commonly accompanied by a sense of shame or self-stigmatization. Self-stigmatization results from public stigmatization in a process leading to the internalization of the social opprobrium attaching to the negative stereotypes associated with addiction. We offer an account of how this process works in terms of a range of looping effects, and this leads to our main claim that for a significant range of cases public stigma figures in the social construction of addiction. This rests on a social constructivist account in which those affected by public stigmatization internalize its norms. Stigma figures as part-constituent of the dynamic process in which addiction is formed. Our thesis is partly theoretical, partly empirical, as we source our claims about the process of internalization from interviews with people in treatment for substance use problems.

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