TY - JOUR
AU - Bélanger, Mathieu
AU - Marquis, Jean-Pierre
PY - 2013/06/11
Y2 - 2024/07/13
TI - Menger and Nöbeling on pointless topology
JF - Logic and Logical Philosophy
JA - LLP
VL - 22
IS - 2
SE - Articles
DO - 10.12775/LLP.2013.009
UR - https://apcz.umk.pl/LLP/article/view/LLP.2013.009
SP - 145–165
AB - <p>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 First, Menger's geometrical perspective was superseded by an algebraic one, a lattice-theoretical one to be precise.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.</p>
ER -