Relative Borsuk–Ulam Theorems for Spaces with a Free $\mathbb{Z}_2$-action

Volume 61 / 2013

Denise de Mattos, Thaís F. M. Monis, Edivaldo L. dos Santos Bulletin Polish Acad. Sci. Math. 61 (2013), 71-77 MSC: Primary 55M20; Secondary 55M35. DOI: 10.4064/ba61-1-8


Let $(X,A)$ be a pair of topological spaces, $T : X \to X$ a free involution and $A$ a $T$-invariant subset of $X$. In this context, a question that naturally arises is whether or not all continuous maps $f : X \to \mathbb{R}^{k}$ have a $T$-coincidence point, that is, a point $x \in X$ with $f (x) = f (T (x))$. In this paper, we obtain results of this nature under cohomological conditions on the spaces $A$ and $X$.


  • Denise de MattosDepartment of Mathematics
    ICMC – University of São Paulo
    Caixa Postal 668
    13560-970 São Carlos, SP, Brazil
  • Thaís F. M. MonisDepartment of Mathematics
    IGCE – Universidade Estadual Paulista
    Caixa Postal 178
    13506-900 Rio Claro, SP, Brazil
  • Edivaldo L. dos SantosDepartment of Mathematics
    Federal University of São Carlos
    Caixa Postal 676
    13565-905, São Carlos, SP, Brazil

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