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James Raymond Munkres (born August 18, 1930) is a Professor Emeritus of mathematics at MIT [1] and the author of several texts in the area of topology, including Topology (an undergraduate-level text), Analysis on Manifolds, Elements of Algebraic Topology, and Elementary Differential Topology. He is also the author of Elementary Linear Algebra.
The elements of are called simplices ... Allen Hatcher: Algebraic Topology, ... James R. Munkres: . Band 1984. Addison Wesley, Menlo Park, California 1984, ISBN 0-201 ...
Massey, William S. (1991), A Basic Course in Algebraic Topology, Springer, ISBN 038797430X; May, J. Peter (1999), A Concise Course in Algebraic Topology, ISBN 9780226511832; Deane Montgomery and Leo Zippin, Topological Transformation Groups, Interscience Publishers (1955) Munkres, James R. (2000), Topology, Prentice Hall, ISBN 0-13-181629-2
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...
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 ...
That is, every element of τ 1 is also an element of τ 2. Then the topology τ 1 is said to be a coarser (weaker or smaller) topology than τ 2, and τ 2 is said to be a finer (stronger or larger) topology than τ 1. [nb 1] If additionally we say τ 1 is strictly coarser than τ 2 and τ 2 is strictly finer than τ 1. [1]
The barycentric subdivision is an operation on simplicial complexes. In algebraic topology it is sometimes useful to replace the original spaces with simplicial complexes via triangulations: This substitution allows one to assign combinatorial invariants such as the Euler characteristic to the spaces.
Pseudocircle − A finite topological space on 4 elements that fails to satisfy any separation axiom besides T 0. However, from the viewpoint of algebraic topology, it has the remarkable property that it is indistinguishable from the circle.