Magic mirrors, dense diameters, Baire category

2014/03/02 by Imre Bárány, Bárány, Imre, Miklós Laczkovich +1 · 1 citation
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Limits and Structures in Graph Theory #Metric Geometry (math.MG) #Primary 52A10 #secondary 54E52

paper · pdf · doi:10.48550/arxiv.1403.0246

openalex publication_date 2014/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An old result of Zamfirescu says that for most convex curves C in the plane most points in R² lie on infinitely many normals to C, where most is meant in Baire category sense. We strengthen this result by showing that `infinitely many' can be replaced by `contiunuum many' in the statement. We present further theorems in the same spirit.

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