How to use topology in a sentence

Examples of topology by meaning

More sentences with topology

• In the discrete topology all sets are open (but they are also all closed).From the entry discrete topology
• He understood geometry well, but algebraic topology was beyond him.From the entry beyond
• An infinite set with discrete topology is not compact.From the entry discrete topology
• Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible.From the entry algebraic topology
• The collection of all possible unions of basis elements of a basis is said to be the topology generated by that basis.From the entry basis
• The topology problem was impossibly difficult.From the entry impossibly
• The Zariski topology allows tools from topology to be used in the study of algebraic varieties, even when the underlying field is not a topological field.From the entry Zariski topology
• There are elegant theorems and deep connections with polytopes, polyhedra, combinatorics, commutative algebra, symplectic geometry, and topology.2024, David A. Cox, John B. Little, Henry K. Schenck, Toric Varieties, American Mathematical Society, →ISBN. From the entry toric
• We study tightness properties and selective versions of separability in bitopological function spaces endowed with set-open topologies..2016, Alexander V. Osipov, Selma Özçağ, “Variations of selective separability and tightness in function spaces with set open topologies”…. From the entry bitopological
• At low condensate density, the topology of the single-particle bands is transferred to the bogolon dispersion.2015, O. Bleu, D.D. Solnyshkov, G. Malpuech, “Interacting quantum fluid in a polariton topological insulator”, in arXiv. From the entry bogolon
• We emphasize that this chapter is not an introduction to differential topology, but merely a repetitorium.2007, Markus Banagl, Topological Invariants of Stratified Spaces, →ISBN, page 99. From the entry repetitorium
• Highly oscillating sequences converge in the weak topology, i.e., the topology of convergence of integral means.2002, Eduard Feireisl, “Viscous and/or heat conducting compressible fluids”, in Susan Friedlander, Denis Serre, editors, Handbook of…. From the entry oscillating
• Find them, and prove that an operation satisfying them provides another cryptomorphic version of topology 8.1994, Michael Henle, A Combinatorial Introduction to Topology, page 269. From the entry cryptomorphic
• The p-adic topology on K is the topology defined by the p-adic absolute values.1993, Seth Warner, Topological Rings, Elsevier (North-Holland), page 8. From the entry p-adic absolute value
• Skeletoids and absorbers play an important role in infinite-dimensional topology.2020, Howard Cook, Continua: With the Houston Problem Book, page 70. From the entry absorber
• Among multilevel inverters, multistring inverter topology requires less number of switches and DC sources compared with the cascaded two level inverter.2020, Ashok L. Kumar, S.Albert Alexander, Madhuvanthani Rajendran, Power Electronic Converters for Solar Photovoltaic Systems, page 159. From the entry multistring
• Strongly dense sublocales, almost discrete spaces, overlap algebras, constructive topology..2016, Francesco Ciraulo, “Overlap Algebras as Almost Discrete Locales”, in arXiv. From the entry sublocales
• In recent years, new topologies of uranyl peroxide cage clusters have been achieved using carboxyphosphonate and etidronic ligands.2016, Sarah Hickam, Peter C. Burns, “Oxo Clusters of 5f elements”, in Zhiping Zheng, editor, Recent Development in Clusters of Rare Earths…. From the entry etidronic
• We topologize Spec(M) with Zariski topology, which is analogous to that for Spec(R), and consider Max(M) as the induced subspace topology.2015, Habibollah Ansari-Toroghy, Shokoufeh Habibi, “The Zariski topology-graph on the maximal spectrum of modules over commutative rings”…. From the entry topologize
• The Hausdorff metric topology was first discovered by D.2014, James F. Peters, Topology of Digital Images: Visual Pattern Discovery in Proximity Spaces, Springer Science & Business Media, →ISBN…. From the entry Hausdorff metric
• In particular, “singular” is a local notion, where “local” so far was mainly considered with respect to the Zariski topology.2008, Gert-Martin Greuel, Gerhard Pfister, A Singular Introduction to Commutative Algebra, 2nd edition, Springer, page 523. From the entry Zariski topology
• For toposes were invented by Grothendieck in the sixties for specific purposes in algebraic geometry and algebraic topology.1998, Jean-Pierre Marquis, “Book Review: Colin McLarty. Elementary Categories, Elementary Toposes.”, in Notre Dame Journal of Formal…. From the entry axiomatize
• The largest mass objects in the universe are superclusters of galaxies, which have a foam-like topology with "great walls" closing "supervoids".1997, Dark Matter In Astro- And Particle Physics, Dark '96, World Scientific Publishing Company, →ISBN, page 412. From the entry supervoid
• A complementary objective is to put this theory into practice: studying functoriality in algebraic topology, naturality in group theory, and universal properties in algebra.2016, Emily Riehl, Category Theory in Context (Aurora: Dover modern math originals), New York: Dover, →ISBN, →OCLC, archived from the…. From the entry diagram chasing
• Soft elastic substrates with a wave-like topology were micromolded from polydimethylsiloxane (PDMS) and fluorescent marker beads were distributed homogeneously in the substrate.2016, Jerome R. Soine, Nils Hersch, Georg Dreissen, Nico Hampe, Bernd Hoffmann, Rudolf Merkel, Ulrich S. Schwarz, “Measuring cellular…. From the entry micromolded
• Thirdly, we have shown that the network topology also fulfils the constraints resulting from the equivalence assumption of the basal and hyperrepressed phenotypes.2015 July 23, Kaveh Pouran Yousef et al., “Logical-continuous modelling of post-translationally regulated bistability of curli fiber…. From the entry hyperrepressed
• However, the classical fronthauling method demands for large bandwidth, low latency, and tightly synchronized on the transport network, and only allows for point-to-point logical topology.2015, Jingchu Liu, Shugong Xu, Sheng Zhou, Zhisheng Niu, “Redesigning Fronthaul for Next-Generation Networks: Beyond Baseband Samples and…. From the entry fronthauling
• Actually a soft ditopological space is a soft set with two independent structures on it - a soft topology and a soft co-topology.2015, Tugbahan Simsekler Dizman, Alexander Sostak, Saziye Yuksel, “Soft Ditopological Spaces”, in arXiv. From the entry ditopological
• This topology has been used in a number of areas such as function space topologies, approximation theory, and optimisation (see, e.g., 22).2014, James F. Peters, Topology of Digital Images: Visual Pattern Discovery in Proximity Spaces, Springer Science & Business Media, →ISBN…. From the entry Hausdorff metric
• When X is a noetherian sober space the construction of loc. cit. can be extended to an arbitrary lower-semicontinuous function for the constructible topology.2004, Ofer Gabber, “Notes on some t-structures”, in Alan Adolphson, Francesco Baldassarri, Pierre Berthelot, Nicholas Katz, François…. From the entry sober space
• Over the course of a century, one will rise by up to 7 metres, and expand across the sea floor, following the contours and topology of what already exists.2022, Thomas Halliday, Otherlands, Penguin, published 2023, page 143. From the entry bioherm
• Topology of the HCoV-NL63 M protein has not been assessed yet, but one may assume that alphacoronaviral M proteins may adopt Nₑₓₒ-Cₑₓₒ topology allowing for C-terminal modification.2018 September 5, Naskalska A, Dabrowska A, Nowak P, Szczepanski A, Jasik K, Milewska A, et al., “Novel coronavirus-like particles…. From the entry alphacoronaviral
• The path dependence of the interchange is all important since it relates the quantum mechanical concept of particle statistics to the topology of the configuration space.2005, Avinash Khare, Fractional Statistics and Quantum Theory, 2nd edition, World Scientific, page 5. From the entry particle statistics
• The material in Chapters 7 (Obstruction Theory and Eilenberg-MacLane Spaces) and 8 (Bordism, Spectra, and Generalized Homology) introduces the student to the modern perspective in algebraic topology.2001, James F. Davis, Paul Kirk, Lecture Notes in Algebraic Topology, American Mathematical Society, page xii. From the entry algebraic topology
• In Minkowski space-time there is, indeed, a topology definable solely in terms of the causal connectivity among events, the Alexandrov topology, which is provably equivalent to the ordinary manifold topology.1990, Palle Yourgrau, Demonstratives, Oxford University Press, page 252. From the entry Alexandrov topology

Meaning of topology

1. noun The branch of mathematics dealing with those properties of a geometrical object (of arbitrary dimensionality) that are unchanged by continuous deformations (such as stretching, bending, etc., without tearing or gluing).
2. noun Any collection τ of subsets of a given set X that contains both the empty set and X, and which is closed under finitary intersections and arbitrary unions.
3. noun The anatomical structure of part of the body.

Full definition of topology

More about topology

• Meaning of topology
• Plural of topology
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• Topology in Marathi
• Topology in Urdu

Questions about topology in a sentence

How do you use topology in a sentence?

Topology is used as a noun. For example: “The subsets of a set X which constitute a topology are called the open sets of X.”

What is a short sentence with topology?

“The topology problem was impossibly difficult.”

What does topology mean?

Topology means the branch of mathematics dealing with those properties of a geometrical object (of arbitrary dimensionality) that are unchanged by continuous deformations (such as stretching, bending, etc., without tearing or gluing).