What is "analysis situs"

n. (context obsolete mathematics English) topology

n. the branch of pure mathematics that deals only with the properties of a figure X that hold for every figure into which X can be transformed with a one-to-one correspondence that is continuous in both directions [syn: topology]

"Analysis Situs" is a seminal mathematics paper that Henri Poincaré published in 1895. Poincaré published five supplements to the paper between 1899 and 1904.

These papers provided the first systematic treatment of topology and revolutionized the subject by using algebraic structures to distinguish between non- homeomorphic topological spaces, founding the field of algebraic topology. Poincaré's papers introduced the concepts of the fundamental group and simplicial homology, provided an early formulation of the Poincaré duality theorem, introduced the Euler–Poincaré characteristic for chain complexes, and raised several important conjectures, including one named after him which was later proven as a theorem.

Analysis situs may refer to:

• Topology, originally called analysis situs, but the term is now obsolete
• "Analysis Situs" (paper), an 1895 article on topology by Henri Poincaré
• Analysis Situs (book), a 1922 book on topology by Oswald Veblen

Analysis Situs is a book by the Princeton mathematician Oswald Veblen, published in 1922. It is based on his 1916 lectures at the Cambridge Colloquium of the American Mathematical Society. The book, which went into a second edition in 1931, was the first English-language textbook on topology, and served for many years as the standard reference for the domain. Its contents were based on the work of Henri Poincaré as well as Veblen's own work with his former student and colleague, James Alexander.

Among the many innovations in the book was the first definition of a topological manifold, and systematisations of Betti number, torsion, the fundamental group, and the topological classification problem.