On Topology I

"Topology is geometry without distance or angle. The geometrical objects of study, not rigid but rather made of rubber or elastic, are especially stretchy." (Stephen Huggett & David Jordan, “A Topological Aperitif”, 2009)

“In geometry, topology is the study of properties of shapes that are independent of size or shape and are not changed by stretching, bending, knotting, or twisting.” (M C Escher, 1971)

“Topology is the property of something that doesn't change when you bend it or stretch it as long as you don't break anything.” (Edward Witten)

"Topology is the science of fundamental pattern and structural relationships of event constellations." (R Buckminster Fuller)

“Topology is an elastic version of geometry that retains the idea of continuity but relaxes rigid metric notions of distance.” (Samuel Eilenberg)

"Topology is precisely that mathematical discipline which allows a passage from the local to the global." (René Thom)

"In these days the angel of topology and the devil of abstract algebra fight for the soul of every individual discipline of mathematics." (Hermann Weyl)

“The geometry of Algebraic Topology is so pretty, it would seem a pity to slight it and miss all the intuition which it provides. At deeper levels, algebra becomes increasingly important, so for the sake of balance it seems only fair to emphasize geometry at the beginning.” (Allen Hatcher)