On Infinite Kuratowski Theorems

Luis Boza1, Maria Teresa Davila1, Eugenio M.Fedriani2, Rafael Moyano3
1Departamento de Matematica Aplicada I. Univ. de Sevilla. Avda Reina Mercedes 2, 41012-SEVILLA.
2Departamento de Economfa y Empresa. Univ. Pablo de Olavide. Ctra. de Utrera, Km.1. 41013-SEVILLA.
3Departamento de Matemitica Aplicada I. Univ. de Sevilla. Avda Reina Mercedes 2, 41012-SEVILLA.

Abstract

Siri and Gvozdjak proved in [9] that the bananas surface, the pseudosurface consisting in the \(2\)-amalgamation of two spheres, does not admit a finite Kuratowski Theorem.

In this paper we prove that pseudosurfaces arising from the \(n\)-amalgamation of two closed surfaces, \(n \geq 2\), do not admit a finite Kuratowski Theorem, by showing an infinite family of minimal non-embeddable graphs.