# Ambiguous loci of the farthest distance mapping from compact convex sets

Studia Mathematica (1995)

- Volume: 112, Issue: 2, page 99-107
- ISSN: 0039-3223

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topDe Blasi, F., and Myjak, J.. "Ambiguous loci of the farthest distance mapping from compact convex sets." Studia Mathematica 112.2 (1995): 99-107. <http://eudml.org/doc/216147>.

@article{DeBlasi1995,

abstract = {Let be a strictly convex separable Banach space of dimension at least 2. Let K() be the space of all nonempty compact convex subsets of endowed with the Hausdorff distance. Denote by $K^0$ the set of all X ∈ K() such that the farthest distance mapping $a ↦ M_X(a)$ is multivalued on a dense subset of . It is proved that $K^0$ is a residual dense subset of K().},

author = {De Blasi, F., Myjak, J.},

journal = {Studia Mathematica},

keywords = {convex sets; farthest points; distance mapping},

language = {eng},

number = {2},

pages = {99-107},

title = {Ambiguous loci of the farthest distance mapping from compact convex sets},

url = {http://eudml.org/doc/216147},

volume = {112},

year = {1995},

}

TY - JOUR

AU - De Blasi, F.

AU - Myjak, J.

TI - Ambiguous loci of the farthest distance mapping from compact convex sets

JO - Studia Mathematica

PY - 1995

VL - 112

IS - 2

SP - 99

EP - 107

AB - Let be a strictly convex separable Banach space of dimension at least 2. Let K() be the space of all nonempty compact convex subsets of endowed with the Hausdorff distance. Denote by $K^0$ the set of all X ∈ K() such that the farthest distance mapping $a ↦ M_X(a)$ is multivalued on a dense subset of . It is proved that $K^0$ is a residual dense subset of K().

LA - eng

KW - convex sets; farthest points; distance mapping

UR - http://eudml.org/doc/216147

ER -

## References

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