T1-Separation in a category

Abstract

A general notion of T₁-separation with respect to a closure operator is introduced in an arbitrary category. This is done by specializing a previously introduced diagram of Galois connections. This naturally yields a dual notion of T₁-coseparation. These two concepts are studied and related to the notions of separation, coseparation, connectedness and disconnectedness.

Keywords: closure operator, Galois connection, T₁-separation, T₁-coseparation, connectedness, disconnectedness

Quaestiones Mathematicae 29(2006), 151–170