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James Waddell Alexander II (September 19, 1888 – September 23, 1971) was a mathematician and topologist of the pre-World War II era and part of an influential Princeton topology elite, which included Oswald Veblen, Solomon Lefschetz, and others.
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence. Although algebraic topology primarily uses algebra to study topological ...
William Schumacher Massey (August 23, 1920 [1] – June 17, 2017) was an American mathematician, known for his work in algebraic topology. The Massey product is named for him. He worked also on the formulation of spectral sequences by means of exact couples, and wrote several textbooks, including A Basic Course in Algebraic Topology (ISBN 0-387 ...
Legacy.com is a United States–based website founded in 1998, [2] the world's largest commercial provider of online memorials. [3] The Web site hosts obituaries and memorials for more than 70 percent of all U.S. deaths. [4] Legacy.com hosts obituaries for more than three-quarters of the 100 largest newspapers in the U.S., by circulation. [5]
Peter J. Hilton, Shaun Wylie, Homology theory: An introduction to algebraic topology, Cambridge University Press, New York, 1960. [37] ISBN 0-521-09422-4 MR 0115161 Peter Hilton, Homotopy theory and duality , Gordon and Breach, New York-London-Paris, 1965 ISBN 0-677-00295-5 MR 0198466
Absolutely closed See H-closed Accessible See . Accumulation point See limit point. Alexandrov topology The topology of a space X is an Alexandrov topology (or is finitely generated) if arbitrary intersections of open sets in X are open, or equivalently, if arbitrary unions of closed sets are closed, or, again equivalently, if the open sets are the upper sets of a poset.
In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of n-dimensional simplicial complexes.For the most reasonable finite-dimensional spaces (such as compact manifolds, finite simplicial complexes or CW complexes), the sequence of Betti numbers is 0 from some point onward (Betti numbers vanish above the dimension of a space), and they ...
On algebraic topology: 1895. Analysis Situs (PDF), archived (PDF) from the original on 27 March 2012. The first systematic study of topology. On celestial mechanics: 1890. Poincaré, Henri (2017). The three-body problem and the equations of dynamics: Poincaré's foundational work on dynamical systems theory. Translated by Popp, Bruce D. Cham ...