Definition
Topology is a sub-branch of geometry, concerned with relationships between objects that remain unchanged under certain types of deformation (such as stretching, bending, twisting, and shrinking). Objects that can be transformed into each other under such transformations are topologically equivalent. The two objects are then said to be homeomorphic. In a general sense, homeomorphism is a function that provides a mapping between two objects which are topological equivalent.
Introduction
Compared to geometry, topology is a relatively recent field of study. It emerged only in the eighteenth century based on the pioneering works of Leonhard Euler and Gottfried Leibniz, but became quickly an important and independent field of study (e.g., Earl 2019). While geometry is the study of objects in space, topology is the study of how objects are connected, in a more abstract point of view. In geology, these relationships are often derived from geological events in the local history –...
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Bibliography
Burns K (1975) Analysis of geological events. J Int Assoc Math Geol 7:295–321
Clementini E, Di Felice P (1996) A model for representing topological relationships between complex geometric features in spatial databases. Inf Sci 90:121–136
Collon P, Bernasconi D, Vuilleumier C, Renard P (2017) Statistical metrics for the characterization of karst network geometry and topology. Geomorphology 283:122–142
Earl R (2019) Topology: a very short introduction. Oxford University Press, Oxford
Egenhofer MJ, Herring J (1990) Categorizing binary topological relations between regions, lines, and points in geographic databases. The 9:76
Jessell M, Ogarko V, de Rose Y, Lindsay M, Joshi R, Piechocka A, Grose L, de la Varga M, Ailleres L, Pirot G (2021) Automated geological map deconstruction for 3d model construction using map 2loop 1.0 and map 2model 1.0. Geosci Model Dev 14:5063–5092
Li S (2006) A complete classification of topological relations using the 9-intersection method. Int J Geogr Inf Sci 20:589–610
Mantilla R, Troutman BM, Gupta VK (2010) Testing statistical self-similarity in the topology of river networks. J Geophys Res Earth 115(F03038):1–12
Manzocchi T (2002) The connectivity of two-dimensional networks of spatially correlated fractures. Water Resour Res 38:1–1
Nyberg B, Nixon CW, Sanderson DJ (2018) Networkgt: a gis tool for geometric and topological analysis of two-dimensional fracture networks. Geosphere 14:1618–1634
Phillips JD, Schwanghart W, Heckmann T (2015) Graph theory in the geosciences. Earth Sci Rev 143:147–160
Sanderson DJ, Nixon CW (2015) The use of topology in fracture network characterization. J Struct Geol 72:55–66
Sanderson DJ, Peacock DC, Nixon CW, Rotevatn A (2019) Graph theory and the analysis of fracture networks. J Struct Geol 125:155–165
Schaaf A, de la Varga M, Wellmann F, Bond CE (2021) Constraining stochastic 3-d structural geological models with topology information using approximate bayesian computation in gempy 2.1. Geosci Model Dev 14:3899–3913
Thiele ST, Jessell MW, Lindsay M, Ogarko V, Wellmann F, Pakyuz-Charrier E (2016) The topology of geology 1: topological analysis. J Struct Geol 91:27–38
Zlatanova S, Rahman AA, Shi W (2004) Topological models and frameworks for 3d spatial objects. Comput Geosci 30:419–428
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Wellmann, F. (2022). Topology in Geosciences. In: Daya Sagar, B., Cheng, Q., McKinley, J., Agterberg, F. (eds) Encyclopedia of Mathematical Geosciences. Encyclopedia of Earth Sciences Series. Springer, Cham. https://doi.org/10.1007/978-3-030-26050-7_463-1
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DOI: https://doi.org/10.1007/978-3-030-26050-7_463-1
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