L. Kleprlík, A. O. Molchanova, T. Roskovec, “Example of a smooth homeomorphism violating the Luzin <nobr>$N^{-1}$</nobr> property”, Sibirsk. Mat. Zh., 2019, Volume 60, Number 5,Pages <nobr>1133

This article is cited in 1 paper

Example of a smooth homeomorphism violating the Luzin $N^{-1}$ property

L. Kleprlík^a, A. O. Molchanova^bc, T. Roskovec^da

^a Czech Technical University in Prague, Prague, Czech Republic
^b Sobolev Institute of Mathematics, Novosibirsk, Russia
^c University of Vienna, Vienna, Austria
^d University of South Bohemia, České Budějovice, Czech Republic

Abstract: This paper discusses some results concerning the validity of the Luzin $N$ and $N^{-1}$ properties for homeomorphisms. Also, we present a counterexample in the form of a $C^{\infty}$-homeomorphism that violates the $N^{-1}$ property.

Keywords: Luzin property, smooth homeomorphism.

UDC: 517.518+517.51

Received: 12.02.2019
Revised: 04.03.2019
Accepted: 12.03.2019

DOI: 10.33048/smzh.2019.60.510