Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 73-82

BOUNDEDNESS OF PRETANGENT SPACES TO GENERAL METRIC SPACES

Viktoriia Bilet and Oleksiy Dovgoshey

National Academy of Sciences of Ukraine, Institute of Applied Mathematics and Mechanics
Roza Luxemburg str. 74, Donetsk 83114, Ukraine; biletvictoriya 'at' mail.ru

National Academy of Sciences of Ukraine, Institute of Applied Mathematics and Mechanics
Roza Luxemburg str. 74, Donetsk 83114, Ukraine; aleksdov 'at' mail.ru

Abstract. Let (X,d,p) be a metric space with a metric d and a marked point p. We define the set of w-strongly porous at 0 subsets of [0,\infty) and prove that the distance set {d(x,p): x \in X} is w-strongly porous at 0 if and only if every pretangent space to X at p is bounded.

2010 Mathematics Subject Classification: Primary 54E35, 28A10.

Key words: Metric spaces, infinitesimal boundedness in metric spaces, distance set, local strong porosity.

Reference to this article: V. Bilet and O. Dovgoshey: Boundedness of pretangent spaces to general metric spaces. Ann. Acad. Sci. Fenn. Math. 39 (2014), 73-82.

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doi:10.5186/aasfm.2014.3902