Non-Linear Images of \(\mu\)-Shadings, Shadings in \(\mathbb{R}^2\), and Quotient Sets of \(\mu\)-Shadings

Abstract

In the paper we prove that some natural modifications (for instance, images under some functions, Cartesian products, quotient sets) of certain types of \(\mu\)-shadings (or shadings), are other examples of \(\mu\)-shadings (or shadings). The studies of shadings and \(\mu\)-shadings were initiated by R. Mabry in 1990. Our work is a continuation of his and K. Neu's research in this field. In particular, we solve one problem posed by R. Mabry.