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).


 * If geometry is dressed in a suit coat, topology dons jeans and a T-shirt.


 * 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.


 * 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.