Abstract

This paper looks at how the idea of pointless topology itself evolved during its pre-localic phase by analyzing the definitions of the concept of topological space of Menger and Nöbeling. Menger put forward a topology of lumps in order to generalize the definition of the real line. As to Nöbeling, he developed an abstract theory of posets so that a topological space becomes a particular case of topological poset. The analysis emphasizes two points. First, Menger's geometrical perspective was superseded by an algebraic one, a lattice-theoretical one to be precise. Second, Menger's bottom–up approach was replaced by a top–down one