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...ogy#Computational homology|computational homology]].<ref>{{Cite book|title=Computational homology|first=Tomasz|last=Kaczynski|date=2004|publisher=Springer|others=Mi ...ing]]'s [[house with two rooms]] and [[Christopher Zeeman]]'s [[Dunce hat (topology)|dunce hat]]; they are [[contractible]] (homotopy equivalent to a point), b ...

...ffset filtration]].<ref name = ghrist>{{Cite book|title=Elementary applied topology|last=Ghrist|first=Robert W.|date=2014|isbn=9781502880857|edition=1st|locati * [[Computational geometry]] ...

...natorics''' is the application of [[topology|topological]] and [[algebraic topology|algebro-topological]] methods to solving problems in [[combinatorics]]. ...gy and in the early 20th century this turned into the field of [[algebraic topology]]. ...

{{Short description|Computational problem in algebraic topology}} ...ion 5 or more.<ref>{{citation |last=Stillwell |first=John |title=Classical Topology and Combinatorial Group Theory |url=https://books.google.com/books?id=265lb ...

...to smoothly join other [[Surface (topology)|surface]]s together, and in [[computational mechanics]] applications, particularly in [[finite element method]] and [[b * [[Surface (topology)|Surface]] ...

{{Short description|Concept in topology}} ...ber, M.|title=Topological complexity of motion planning|journal=Discrete & Computational Geometry|volume=29 |issue=2|pages= 211–221|year=2003}} ...

{{Short description|Computational tool}} ...'''Toda–Smith complexes'''<!-- Who are Toda and Smith? --> are [[spectrum (topology)|spectra]] characterized by having a particularly simple [[Brown–Peterson c ...

...m/10.1007/s41468-022-00110-9 |journal=Journal of Applied and Computational Topology |language=en |doi=10.1007/s41468-022-00110-9 |arxiv=2109.05513 |s2cid=23749 ...l=https://link.springer.com/10.1007/s00454-022-00476-8 |journal=Discrete & Computational Geometry |language=en |doi=10.1007/s00454-022-00476-8 |issn=0179-5376|arxiv ...

...topology)|continuous maps]] <math>f: X \to Y</math>, and while equivariant topology also considers such maps, there is the additional constraint that each map ...to any symmetry possessed by both spaces. A famous theorem of equivariant topology is the [[Borsuk–Ulam theorem]], which asserts that every <math>\mathbf{Z}_2 ...

are the [[Connected component (topology)|connected component]]s of sets of the form |title=Handbook of Computational Geometry ...

...ve-url=https://web.archive.org/web/20200223170824/http://www.kovalevsky.de/Topology/Introduction_e.htm#a6 |access-date=November 30, 2021|archive-date=2020-02-2 [[File:SimpleGraf.jpg|thumb|All [[Graph (topology)|graphs]] are ([[Homeomorphism|homeomorphic]] to) 1-dimensional cubical com ...

...omputational topology]]'', which studies the application of computation to topology. ==Topology of lambda calculus== ...

...R., Vegter, G., Kerber, M., Jones, B. J. T., & Wintraecken, M. (2017). The topology of the cosmic web in terms of persistent Betti numbers. ''Monthly Notices o ...=Herbert |url=https://www.worldcat.org/oclc/946298151 |title=Computational topology : an introduction |date=2010 |publisher=American Mathematical Society |othe ...

...=Nelson |first1=Bradley J. |last2=Luo |first2=Yuan |date=2022-01-31 |title=Topology-Preserving Dimensionality Reduction via Interleaving Optimization |class=cs ...les |url=https://doi.org/10.1007/s10208-015-9255-y |journal=Foundations of Computational Mathematics |language=en |volume=15 |issue=3 |pages=613–650 |doi=10.1007/s1 ...

...Series, Vol. 5, [[American Mathematical Society]].</ref> for studying the topology and geometry of [[plane curve|plane curves]]. The three main invariants—<ma ...]] online lecture notes at https://ocw.mit.edu/courses/18-900-geometry-and-topology-in-the-plane-spring-2023/mit18_900s23_lec17.pdf</ref> ...

...irations for [[William Thurston]]'s later breakthroughs in [[3-dimensional topology]].{{sfn|Thurston|1982|p=360}} Riley's research was in [[geometric topology]], especially in [[knot theory]], where he mostly studied [[Representation ...

...c/1129044889 |title=Topological data analysis for genomics and evolution : topology in biology |date=2020 |others=Andrew J. Blumberg |isbn=978-1-316-67166-5 |l ...=Herbert |url=https://www.worldcat.org/oclc/427757156 |title=Computational topology : an introduction |date=2010 |publisher=American Mathematical Society |othe ...

...fset filtration has become a primary example in the study of computational topology and data analysis. ...url=http://link.springer.com/10.1007/s00454-014-9573-x |journal=Discrete & Computational Geometry |language=en |volume=51 |issue=3 |pages=600–627 |doi=10.1007/s0045 ...

...cle/pii/S0925772108001193 Efficient algorithms for computing Reeb graphs], Computational Geometry 42 (2009) 606–616</ref> ...9>{{cite journal |last1=Stanley |first1=Geoffrey J. |title=Neutral surface topology |journal=Ocean Modelling |date=June 2019 |volume=138 |pages=88–106 |doi=10. ...

...tps://link.springer.com/10.1007/s10208-022-09576-6 |journal=Foundations of Computational Mathematics |language=en |doi=10.1007/s10208-022-09576-6 |arxiv=2010.09628 ...ps://www.worldcat.org/oclc/7948164 |title=Introduction to piecewise-linear topology |date=1982 |publisher=Springer-Verlag |others=B. J. Sanderson |isbn=0-387-1 ...