Topology and Topological Space[box title=”Topics” style=”default” box_color=”#005ce6″ title_color=”#FFFFFF” radius=”3″]
- Introduction to Topology
- Applications of Topology
- What is Topology?
- What is a Euclidean space?
- Euclidean Axioms to Topological Axioms
- What is an Open Set & Open Interval?
- Who was Pavel Sergeyevich Alexandrov?
- Proof of Topology and Topological Space through Axioms
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
- Topology – James R. Munkres
- Topology without tears – Sidney A.Morris
- Richard Sot (PhD. Mathematics, University of Rochester, Rochester, NY)
Shounak Bhattacharya is working as a Director, Training and Placement Department for Asian College of Teachers, Thailand. Apart from training, he is a researcher as well as a teacher in the area of
- Tensor analysis,
- General theory of relativity,
- Differential geometry and
- Introductory topology.
Shounak has been researching and educating the global crowd in the area of building career opportunities through teaching, researching, and communicating. Working with Asian College of Teachers, his main focus has been increasing employability factors among young students. The path leads to many factors including teaching, researching, communicating as well as creating a unique model which would employ the right person for the right job.
Relentlessly working in simplifying difficult mathematical concepts, Shounak’s interest revolves around Einstein’s general theory of relativity and creating structures, models, videos to educate the mass. He has been in touch with Prof. Lohiya, a former student of Dr. Stephen Hawking, and has conducted interviews regarding his experience working with Stephen Hawking.
He is working under the guidance of Dr.Richard Sot, Ph.D. Mathematics, University of Rochester, NY and Dr.Santosh Karn, Ph.D., Physics from Delhi University.
He has held numerous live interviews with researchers, educators, teachers, and dignitaries around the globe primarily,
- The United Kingdom,
- Australia and
He is a professional translator of the Arabic language, certified from RMIC. He is currently into Persian-Urdu translation of literary texts and creating videos on complex mathematical concepts.