nLab Analysis Situs

Context

Topology

topology (point-set topology, point-free topology)

see also differential topology, algebraic topology, functional analysis and topological homotopy theory

Introduction

Basic concepts

Universal constructions

Extra stuff, structure, properties

Examples

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

Algebraic topology

Homotopy theory

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

This page is about the article

which initiated (cf. Stillwell p. 6) the modern fields of topology (such as in introducing the notion and terminology of homeomorphisms), of algebraic topology (introducing singular homology) and of homotopy theory (introducing the fundamental group).

See also:

Poincaré took both the term and the basic idea of “analysis situs” from a(n unpublished) proposal that Gottfried Leibniz had made right after inventing differential calculus:

  • Matthew McMillan: Geometric Quantity in Leibniz’s Analysis Situs, PhD thesis, Oxford (2017) [pdf, pdf]

  • Vincenzo De Risi: Analysis Situs, the Foundations of Mathematics and a Geometry of Space, The Oxford Handbook of Leibniz, Oxford University Press (2018) 247-258 [hal:03059623, doi:10.1093/oxfordhb/9780199744725.013.22]

category: reference

Last revised on November 21, 2024 at 07:52:29. See the history of this page for a list of all contributions to it.