Resumen de Functional topology for geometric settings

Wendy Lowen, Joris Mestdagh

• In this paper we propose two approaches to connect the functional topology theory of Clementino et al. (2004) [4] with the situation in the category Sch of schemes. In a first approach, we extend an example from [4] to a more general pattern for obtaining a class of ��closed morphisms�� from two auxiliary classes, ��closed embeddings�� and newly added ��surjections��. In a second approach we apply [4] to the presheaf category over Sch, and recover the notions of properness and separatedness on Sch.