Applications of Topology

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Topology and Topological Space

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Applications of Topology

 

Topology, similar to any other branch of advanced mathematics is abstract. The question arises, why should I learn topology? What is the use?

 

  • Applications to Digital Image Processing

As we see the digital images, which are an important element of communication. The images that we capture in the digital camera, the ebooks, graphics all involve a space. Digital topology, which is an important aspect, is extensively used, The topological concepts of continuity and connectedness is used in the digital world. As we see the world is continuous and connected and the digital plane is disconnected. To connect both of them, topology is used.

 

  • Application to Physics

General relativity is the one that comes first. The study of curved surfaces, Riemannian manifolds, and various other surfaces requires topology to study. In face general relativity uses topology widely in order to study the surfaces.

 

  • Applications to Biology

Topology plays an important role in Biology also. As genotypes and phenotypes are the primary driving force in biology, topology is being used in order to sequence the right nucleotides in the DNA strand. Genotypes are hidden and are the inheritable information of a living organism, while phenotypes carry the physical appearances. Topology contributes immensely to solve problems in DNA research. We have a concept of metric in topology which, roughly means distance, a function to measure the distance between the elements of sets. The concept of metric space gives us an idea to measure DNA sequences, thus helps us to find the nature of the way species evolve in history.

 

  • Geographic Information System (GIS)

GIS is computer software that has the ability to accumulate, store, operate, and execute geographic information. Topology in GIS is used in analyzing the spatial relationships among different regions in an area. It is used in analyzing how points, lines, and polygons share a boundary.

Next | What is Topology?

 

See Also | More Topology Articles


Further References:

  • Topology – James R. Munkres
  • Topology without tears – Sidney A.Morris

Article Advisor:

  • Richard Sot (PhD. Mathematics, University of Rochester, Rochester, NY)

Website references:

  1. https://mathworld.wolfram.com
  2. https://www.wikipedia.org/
  3. https://math.stackexchange.com/
  4. https://www.researchgate.net/publication/343635292

 

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