Topological meaning in english

1The way in which constituent parts are interrelated or arranged.

‘using distances determined in this manner ignores existing road conditions and topology that can potentially affect travel time and costs’

• ‘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.’
• ‘A ring network is a topology of computer networks where each user is connected’
• ‘This result is not merely a sampled version of Fig 7A; rather, it incorporates the constraints imposed by the edge distributions on the topology of the network.’
• ‘Although this relationship may vary between species, for a particular species it is constant, indicating that the polarity of the pollen grain owes its origin to the topology of microspore tetrad formation.’
• ‘The stoichiometry matrix: Structural modelling in this context is so called because the focus is on the network topology of the system.’
• ‘Other than an unresolved reticulation at the most ancestral node, the topology of this network is straightforward and there are three noteworthy results.’
• ‘In this work, the topology of protein domain networks generated with data from the ProDom, Pfam, and Prosite domain databases was studied.’
• ‘After you've installed the Mazu hardware, you need to teach the system about the topology of your internal network.’
• ‘The actual fiber path plays a big part in how the topology of the network will look.’
• ‘This means that the topology of the metabolic network is only partially able to explain the observed data.’
• ‘A schematic of region I of the germarium showing the topology of the germline stem cell region and the expression pattern of genes relevant to this study.’
• ‘I've been doing a lot of stuff at work which is about designing social networks and their topologies, and peterme seems similarly preoccupied.’
• ‘What is the power of a computer which can change the very notion of the topology of the underlying circuit connectivity?’
• ‘As chol was added, the topology of the domains was changed [formation of lo domains], and eventually phase separation disappeared at high chol fractions.’
• ‘The null space of the stoichiometric matrix that describes the topology of metabolic networks and that contains the steady-state flux distributions has been analyzed in detail.’
• ‘We also have no indication that the topology of the phylogenetic trees is biased by the alignments or the tree-building algorithms.’
• ‘Thus, the strength of selective constraints on gene sequences is affected by the topology of the gene coexpression network.’
• ‘On a molecular level, stress relaxation occurs by a change in the topology of the connections within the skeletal network.’

2Mathematics
mass noun 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.’
• ‘This book is a classic in the study of the geometric topology of 3-manifolds.’
• ‘His research interests include topology, algebraic geometry, and Lie theory.’
• ‘For example, algebraic geometry, the field I am most familiar with, combines algebra, geometry, topology, and analysis.’
• ‘He started research in algebra, geometry and topology as a student but did not consider his results sufficiently important to merit publication.’
• ‘Geometry, topology, and algebraic geometry and group theory, almost anything you want, seems to be thrown into the mixture.’
• ‘He established a geometry and topology based on group theory without the concept of a limit.’
• ‘Celestial mechanics is the origin of dynamical systems, linear algebra, topology, variational calculus and symplectic geometry.’
• ‘He was always full of mathematical ideas, not only on game theory, but in geometry and topology as well.’
• ‘Ktheory is a mathematical theory that studies topology using matrices, using operators that don't commute with each another.’
• ‘All mathematicians in geometry, complex analysis, low-dimensional topology, and geometric group theory will want to have it on their bookshelves.’
• ‘He worked in a wide variety of mathematical areas including general topology, topological vector spaces, algebraic geometry, invariant theory and the classical groups.’
• ‘His aim was to bring together point-set topology and algebraic topology with his 1932 paper.’
• ‘For my Ph.D. 1 was required to study analysis, algebra, and algebraic topology.’
• ‘They relate Boolean algebras to general topology and to the theory of rings and ideals, and include what is called Stone-tech compactification today.’
• ‘The mathematical ballistics of 1918 was neither as refined as axiomatic geometry nor as theoretical as algebraic topology.’
• ‘His main work was in set theory, general topology, and measure theory.’
• ‘The largest number of paper-cutting/tearing opportunities related to Ending the sum of the interior angles in a triangle along with spatial visualization and topology.’