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.

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

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.