An involution of reals, discontinuous on rationals, and whose derivative vanishes a.e.

ULUDAĞ A. M., Ayral H.

TURKISH JOURNAL OF MATHEMATICS, vol.43, no.3, pp.1770-1775, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 3
  • Publication Date: 2019
  • Doi Number: 10.3906/mat-1903-34
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1770-1775
  • Keywords: Involution, PGL, projective general linear group, continued fraction, derivative, discontinuity
  • Galatasaray University Affiliated: Yes

Abstract

We study the involution of the real line, induced by Dyer's outer automorphism of PGL(2,Z). It is continuous at irrationals with jump discontinuities at rationals. We prove that its derivative exists almost everywhere and vanishes almost everywhere.