Out of Context: On Topology (Definitions)

"Topology is the study of topological properties and, especially, topological invariants of figures." (Maurice Frechet & Ky Fan, "Initiation to Combinatorial Topology", 1967)

"Topology is the science of fundamental pattern and structural relationships of event constellations." (R Buckminster Fuller, "Operating Manual for Spaceship Earth", 1969)

"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 not ‘designed to guide us’ in structure. It is this structure." (Jacques Lacan, "L’Étourdit", 1972)

"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, [interview] 2003)

"Topology is the mathematical study of properties of objects which are preserved through deformations, twistings, and stretchings but not through breaks or cuts." (David Robinson & David Goforth, "The Topology of the 2×2 Games: A New Periodic Table". 2005)

"Topology is geometry without distance or angle." (Stephen Huggett & David Jordan, "A Topological Aperitif", 2009)

"[…] topology is the study of those properties of geometric objects which remain unchanged under bi-uniform and bi-continuous transformations." (Lokenath Debnath, "The Legacy of Leonhard Euler - A Tricentennial Tribute", 2010)

"Topology, then, is really a mathematics of relationships, of unchangeable, or 'invariant', patterns." (Fritjof Capra, "The Systems View of Life: A Unifying Vision", 2014)

"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)

"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)