Singular points for tilings of normed spaces

Vladimir P. Fonf, Antonio Pezzotta, Clemente Zanco

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

A point x in a normed space X is said to be singular for a given tiling of X whenever each neighborhood of x intersects infinitely many tiles. We show that, when X is infinite-dimensional and all tiles are convex, special points in the boundary of tiles (like extreme points or PC points, if any) must be singular. Under the further assumptions that X is separable and doesn’t contain c0, singular points abound among the smooth points of any bounded tile. Finally, in any normed space a tiling is constructed which is free of singular points and whose members are both bounded and star-shaped; this disproves the conjecture that Corson’s theorem might apply to star-shaped bounded coverings.

Original languageEnglish
Pages (from-to)857-868
Number of pages12
JournalRocky Mountain Journal of Mathematics
Volume30
Issue number3
DOIs
StatePublished - 1 Jan 2000

Keywords

  • Convex tile
  • Singular point
  • Tiling of normed space

ASJC Scopus subject areas

  • Mathematics (all)

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