Topology

In mathematics, topology is concerned with the properties of space that are preserved under continuous deformations, such as bending, twisting, stretching, and squashing, but not tearing or gluing.

Quotes

• Presentday topology consists of two distinct parts: point set topology and algebraic topology. The first has mainly been the prerogative of Poland plus a strong American component: the school of R. L. Moore (of Austin, Texas).
  • I. M. James (24 August 1999). History of Topology. Elsevier. p. 544. ISBN 978-0-08-053407-7. 

• If geometry is dressed in a suit coat, topology dons jeans and a T-shirt.
  • David S. Richeson (8 March 2012). Euler's Gem: The Polyhedron Formula and the Birth of Topology. Princeton University Press. p. 9. ISBN 1-4008-3856-8. 

• Topologists are interested not only in finite-dimensional spaces (for example, subspaces of Rⁿ), but also in infinite-dimensional ones, such as the spaces occurring in quantum field theory.
  • Albert S. Schwarz (16 July 1996). Topology for Physicists. Springer Science & Business Media. p. 23. ISBN 978-3-540-54754-9. 

• In these days the angel of topology and the devil of abstract algebra fight for the soul of each individual mathematical domain.
  • Weyl, Hermann. Invariants. Duke Math. J. 5 (1939), no. 3, 489--502. doi:10.1215/S0012-7094-39-00540-5. http://projecteuclid.org/euclid.dmj/1077491405.

External links

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Topology

Mathematics
Mathematicians (by country)	Abel • Anaxagoras • Archimedes • Aristarchus of Samos • Averroes • Arnold • Banach • Cantor • Cartan • Chern • Cohen • Descartes • Diophantus • Erdős • Euclid • Euler • Fourier • Gauss • Gödel • Grassmann • Grothendieck • Hamilton • Hilbert • Hypatia • Lagrange • Laplace • Leibniz • Milnor • Newton • von Neumann • Noether • Penrose • Perelman • Poincaré • Pólya • Pythagoras • Riemann • Russell • Schwartz • Serre • Tao • Tarski • Thales • Turing • Weil • Weyl • Wiles • Witten
Numbers	1 • 23 • 360 • e • π • Fibonacci numbers • Irrational number • Negative number • Number • Prime number • Quaternion • Octonion
Concepts	Abstraction • Algorithms • Axiomatic system • Completeness • Deductive reasoning • Differential equation • Dimension • Ellipse • Elliptic curve • Exponential growth • Infinity • Integration • Geodesic • Induction • Proof • Partial differential equation • Principle of least action • Prisoner's dilemma • Probability • Randomness • Theorem • Topological space • Wave equation
Results	Euler's identity • Fermat's Last Theorem
Pure math	Abstract algebra • Algebra • Analysis • Algebraic geometry (Sheaf theory) • Algebraic topology • Arithmetic • Calculus • Category theory • Combinatorics • Commutative algebra • Complex analysis • Differential calculus • Differential geometry • Differential topology • Ergodic theory • Foundations of mathematics • Functional analysis • Game theory • Geometry • Global analysis • Graph theory • Group theory • Harmonic analysis • Homological algebra • Invariant theory • Logic • Non-Euclidean geometry • Nonstandard analysis • Number theory • Numerical analysis • Operations research • Representation theory • Ring theory • Set theory • Sheaf theory • Statistics • Symplectic geometry • Topology
Applied math	Computational fluid dynamics • Econometrics • Fluid mechanics • Mathematical physics • Science
History of math	Ancient Greek mathematics • Euclid's Elements • History of algebra • History of calculus • History of logarithms • Indian mathematics • Principia Mathematica
Other	Mathematics and mysticism • Mathematics education • Mathematics, from the points of view of the Mathematician and of the Physicist • Philosophy of mathematics • Unification in science and mathematics