Geodesic
Relative Borsuk–Ulam Theorems for Spaces with a Free $\mathbb{Z}_2$-action
Denise de Mattos1 ; Thaís F. M. Monis2 ; Edivaldo L. dos Santos3
1 Department of Mathematics ICMC – University of São Paulo Caixa Postal 668 13560-970 São Carlos, SP, Brazil
2 Department of Mathematics IGCE – Universidade Estadual Paulista Caixa Postal 178 13506-900 Rio Claro, SP, Brazil
3 Department of Mathematics Federal University of São Carlos Caixa Postal 676 13565-905, São Carlos, SP, Brazil
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 61 (2013) no. 1, pp. 71-77

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $X$.
DOI : 10.4064/ba61-1-8
Keywords: pair topological spaces involution t invariant subset context question naturally arises whether continuous maps mathbb have t coincidence point point paper obtain results nature under cohomological conditions spaces

Denise de Mattos 1 ; Thaís F. M. Monis 2 ; Edivaldo L. dos Santos 3

1 Department of Mathematics ICMC – University of São Paulo Caixa Postal 668 13560-970 São Carlos, SP, Brazil
2 Department of Mathematics IGCE – Universidade Estadual Paulista Caixa Postal 178 13506-900 Rio Claro, SP, Brazil
3 Department of Mathematics Federal University of São Carlos Caixa Postal 676 13565-905, São Carlos, SP, Brazil 
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Denise de Mattos; Thaís F. M. Monis; Edivaldo L. dos Santos. Relative Borsuk–Ulam Theorems for Spaces with a Free $\mathbb{Z}_2$-action. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 61 (2013) no. 1, pp. 71-77. doi: 10.4064/ba61-1-8

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