topology
/təˈpɒlədʒi
/noun (plural topologies)
1 [mass noun] Mathematics The study of geometrical properties and spatial relations unaffected by the continuous change of shape or size of figures.Euclidean geometry studies Euclidean-space-structure, topology studies topological structures, and so on....
- The Poincare conjecture belongs to the field of topology, which studies properties that are preserved when a shape is stretched or twisted without tearing.
- The key divergence from traditional modelling methods was to think of the form as a topological entity, with topology being the study of geometry unaffected by change in scale or shape.
1.1 [count noun] A family of open subsets of an abstract space such that the union and the intersection of any two of them are members of the family, and which includes the space itself and the empty set.A single most parsimonious cladogram was recovered for the ‘archaic’ subset with a topology identical to that seen in all of the MMPC....
- Tree topologies gather together members of the same families and fit the taxonomic classification of these dipteran species.
- Membrane topology of the FNT family members is consistent with six putative transmembrane helical spanning domains, as established for the FOCA protein of E.coli.
2The way in which constituent parts are interrelated or arranged: the topology of a computer network...
- The genealogy can be viewed as consisting of two components: the topology of the tree structure and the times between coalescent events.
- Firstly, if you happen to run an extensive subterranean mass transit system, you should familiarise yourself with the topology of the network.
- We explored forcing our data to conform to the topologies of previous among-group arrangements.
Derivatives
topological
- One of the main problems has been and remains the classification of these algebras as intrinsic algebraic and topological objects.
- The author has succeeded in writing a book understandable to readers with very little knowledge of functional analysis and topological vector spaces.
- This work continued through the early 1930s then in the late 1930s he studied ordered topological vector spaces.
topologically
- For the case of a finite-dimensional real linear space these are infinite systems whose adjoint cone is topologically closed.
- According to embedding theory, the Poincare map is topologically equivalent to a Poincare surface of section that intersects the system's trajectory in its characteristic state-space.
- In particular, he conjectured that any smooth 3-surface that has no edges, no corkscrew-like twists, and no doughnut-like holes must be topologically equivalent to a 3-sphere.
topologist
- When he produced his first few results on 4-manifolds, the ideas were so new and foreign to geometers and topologists that they merely gazed in bewildered admiration.
- In fact, essentially every invariant studied by topologists can be made into a representable or corepresentable functor.
- A simple way to describe topology is as a ‘rubber sheet geometry’ - topologists study those properties of shapes that remain the same when the shapes are stretched or compressed.
Origin
Late 19th century: via German from Greek topos 'place' + -logy.