Archiv der Mathematik

, Volume 69, Issue 4, pp 338–342 | Cite as

On the space of compacta with dense set of points with non-single valued nearest point mapping

  • T. Radul


The function \( p_K: {\Bbb R}^n \to {\rm exp}({\Bbb R}^n) \) called nearest point mapping is well-known: for a given compact set \( K \subset {\Bbb R}^n \), p K associates to each \( x \in {\Bbb R}^n \) the set of all points of K closest to x. T. Zamfirescu has shown that the set \( {\cal K} _p \) consisting of all compacta K, for which p K is non-single valued at densely many points, has the complement in \( {\rm exp}\, {\Bbb R}^n \) of the first Baire category [8]. We show in this paper that the space \( {\cal K}_p \) is homeomorphic to the Hilbert space; moreover, it is contained in \( {\rm exp}\, {\Bbb R}^n \) as the pseudo-interior in the Hilbert cube without some point.


Hilbert Space Point Mapping Baire Category Hilbert Cube 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Verlag, Basel 1997

Authors and Affiliations

  • T. Radul
    • 1
  1. 1.Department of Mechanics and Mathematics, Lviv State University, Universytetska St., 1, UA-290602 Lviv, UkraineUA

Personalised recommendations