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

Authors

ABDURRAHMAN MUHAMMED ULUDAĞ
HAKAN AYRAL

DOI

10.3906/mat-1903-34

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.

Keywords

Involution, PGL, projective general linear group, continued fraction, derivative, discontinuity

First Page

1770

Last Page

1775

Recommended Citation

ULUDAĞ, ABDURRAHMAN MUHAMMED and AYRAL, HAKAN (2019) "An involution of reals, discontinuous on rationals, and whose derivative vanishes a.e.," Turkish Journal of Mathematics: Vol. 43: No. 3, Article 49. https://doi.org/10.3906/mat-1903-34
Available at: https://journals.tubitak.gov.tr/math/vol43/iss3/49