Continuous convexity and canonical partial metrics in normed spaces
Romaguera, S. ; Oltra, S. ; Sánchez Pérez, E.A.
Bull. Belg. Math. Soc. Simon Stevin, Tome 15 (2008) no. 1, p. 547-559 / Harvested from Project Euclid
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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.
Publié le : 2008-05-15
Classification:  partial metric,  normed space,  46B20,  54E35 
@article{1222783099,
     author = {Romaguera, S. and Oltra, S. and S\'anchez P\'erez, E.A.},
     title = {Continuous convexity and canonical partial metrics in normed spaces},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {15},
     number = {1},
     year = {2008},
     pages = { 547-559},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1222783099}
}

Romaguera, S.; Oltra, S.; Sánchez Pérez, E.A. Continuous convexity and canonical partial metrics in normed spaces. Bull. Belg. Math. Soc. Simon Stevin, Tome 15 (2008) no. 1, pp.  547-559. http://gdmltest.u-ga.fr/item/1222783099/