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  1. 1 Logic and Logical Philosophy

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  1. 1 Bélanger M.

  2. 1 Marquis J.-P.

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  1. 1 2013

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Menger and Nöbeling on Pointless Topology

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Bélanger M., Marquis J.-P.
Logic and Logical Philosophy
|
2013
|
vol. 22
|
issue 2
145-165
EN
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 First, Menger’s geometrical perspective was superseded by an algebraic one, a lattice-theoretical one to be precise.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.
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