Topology, or analysis situs, has often been regarded as the study of those properties of point sets (in Euclidean space or in abstract spaces) that are invariant under homeomorphisms. Besides the modern concept of homeomorphism, at least three other concepts were used in this context during the late 19th and early 20th centuries, and regarded (by various mathematicians) as characterizing topology: deformations, diffeomorphisms, and continuous bijections. Poincaré, in particular, characterized analysis situs in terms of deformations in 1892 but in terms of diffeomorphisms in 1895. Eventually Kuratowski showed in 1921 that in the plane there can be a continuous bijection of P onto Q, and of Q onto P, without P and Q being homeomorphic.
...MoreDescription Topology during the late 19th and early 20th centuries.
Article
German A. Duarte;
(2017)
"Analysis Situs." A Survey of Spaces en devenir
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Article
Ullrich, Peter;
(2000)
The Poincaré-Volterra Theorem: From Hyperelliptic Integrals to Manifolds with Countable Topology
(/isis/citation/CBB000740287/)
Book
Epple, Moritz;
(1999)
Die Entstehung der Knotentheorie: Kontexte und Konstruktionen einer modernen mathematischen Theorie
(/isis/citation/CBB000650718/)
Article
Chorlay, Renaud;
(2010)
From Problems to Structures: The Cousin Problems and the Emergence of the Sheaf Concept
(/isis/citation/CBB000932987/)
Article
Moore, Gregory H.;
(2008)
The Emergence of Open Sets, Closed Sets, and Limit Points in Analysis and Topology
(/isis/citation/CBB000950203/)
Book
Ferdinand Verhulst;
(2012)
Henri Poincaré: Impatient Genius
(/isis/citation/CBB160508794/)
Chapter
Schneider, Ivo;
(1999)
Stochastik von Laplace bis Poincaré
(/isis/citation/CBB000450073/)
Book
Charpentier, Éric;
Ghys, Étienne;
Lesne, Annick;
(2010)
The Scientific Legacy of Poincaré
(/isis/citation/CBB001023244/)
Article
Lizhen Ji;
Chang Wang;
(2020)
Poincaré’s stated motivations for topology
(/isis/citation/CBB272091949/)
Article
Roque, Tatiana;
(2015)
L'originalité de Poincaré en mécanique céleste: pratique des solutions périodiques dans un réseau de textes
(/isis/citation/CBB001552876/)
Chapter
Tom Archibald;
(2015)
Saturn’s Rings from Laplace to Poincaré
(/isis/citation/CBB776089038/)
Book
Gray, Jeremy;
(2013)
Henri Poincaré: A Scientific Biography
(/isis/citation/CBB001252495/)
Book
O'Shea, Donal;
(2007)
The Poincaré Conjecture: In Search of the Shape of the Universe
(/isis/citation/CBB000773353/)
Book
Christian Gerini;
Jean-Marc Ginoux;
(2013)
Henri Poincaré: A Biography Through the Daily Papers
(/isis/citation/CBB354216167/)
Article
Craig Fraser;
Michiyo Nakane;
(2023)
Canonical transformations from Jacobi to Whittaker
(/isis/citation/CBB563006808/)
Article
Lizhen Ji;
Chang Wang;
(2022)
Poincaré’s works leading to the Poincaré conjecture
(/isis/citation/CBB001593509/)
Article
Muntersbjorn, Madeline;
(2012)
On the Intellectual Heritage of Henri Poincaré
(/isis/citation/CBB001210329/)
Book
Poincaré, Henri;
Mittag-Leffler, Gösta;
(1999)
Correspondance entre Henri Poincaré et Gösta Mittag-Leffler: Avec en annexes les lettres échangées par Poincaré avec Fredholm, Gyldén et Phragmén
(/isis/citation/CBB000631019/)
Chapter
Jeremy Gray;
(2015)
Henri Poincaré and Hermann Weyl on the Foundations of Mathematics
(/isis/citation/CBB501271170/)
Book
Gray, Jeremy;
(2008)
Plato's Ghost: The Modernist Transformation of Mathematics
(/isis/citation/CBB000950298/)
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