Topology

Möbius strips, which have only one surface and one edge, are a kind of object studied in 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

Wikipedia

Wikipedia has an article about:

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