Topology

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 What is topology? What is topology used for?


Topology is a branch of mathematics that deals with the properties of an object that are invariant (do not change) under continuous deformations like stretching, crushing, coiling. However, shredding or gluing is not allowed. 


It also gives the spatial relation of the elements of a set. In simple words, two objects (spaces) that can be deformed into each other are topologically isomorphic. 


Topology and its types
cube turning into dodecahedron by Tomruen

 

For example, A cube can be deformed into a sphere without breaking it, square into a circle, coffee cup into a torus (doughnut), double doughnut into a kettle, and scissor. 

Fun Fact: It is said that topologists cannot distinguish between a coffee mug and a doughnut.

Types of Topology

Applications of topology:

In mathematics:

It is used in various fields of mathematics such as number theory, differential equations, dynamical systems, knot theory and Riemann surfaces in complex analysis. 

 

In other disciplines:


In biology, it is used in knot theory; in physics, in order to illustrate the space-time structure it is used in string theory, quantum field theory and also to describe the overall shape of the universe in cosmology; in computer science, it is an integral part of the domain theory. 
Location: India
Hey there, This is Hifza Siddiqui, an aspiring Mathematician pursuing masters from the University of Mumbai. I'm writing this blog to share the knowledge and the way I understand mathematics. I hope it helps you to get a better insight. My blog's frequency will be twice per week.

Comments

  1. UnknownJuly 14, 2020 at 5:23 PM

    That's great and indeed of great importance to all the aspirants♥️♥️

    ReplyDelete
  2. MathJuly 14, 2020 at 7:08 PM

    Nice ....keep the up the good spirit👌

    ReplyDelete
  3. UnknownJuly 14, 2020 at 7:53 PM

    Nice one hifza👍👍

    ReplyDelete
  4. UnknownJuly 14, 2020 at 7:55 PM

    Nice one 👍👌

    ReplyDelete
  5. UnknownJuly 14, 2020 at 8:01 PM

    Topology is totally new for me as a statistician, very well explained, which motivated me to study topology (like why, for what and where..)
    Very interesting mathematical concept.🙂
    Good keep it up.✌️✌️

    ReplyDelete
  6. Naimuddin ChoudharyJuly 14, 2020 at 9:52 PM

    Great work keep it up.

    ReplyDelete
  7. UnknownJuly 14, 2020 at 11:05 PM

    It's just simplest and easiest way of explaining topology👌👌.but Can we use it in statistical background.

    ReplyDelete

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