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- 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.
- 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.
- In these days the angel of topology and the devil of abstract algebra fight for the soul of each individual mathematical domain.