Borsuk–Ulam theorems and their parametrized versions for spaces of type $(a,b)$

Abstract

Let $X$ be a space of type $\left(a,b\right)$ equipped with a free $G$–action, with $G={\mathbb{Z}}_2$ or $S^1$. In this paper, we prove some theorems of Borsuk–Ulam-type and the corresponding parametrized versions for such $G$–spaces.