**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

**Pavel Sergeyevich Alexandrov**

A topology in which the intersection of any family of open sets is open is called Alexandrov topology. The Soviet mathematician made an important contribution to the topology.

Alexandrov made his first major mathematical success in 1915 in set theory. He worked with Felix Hausdorff and developed what we call today, point-set topology or general topology. In 1920 he developed “combinatorial topology.” He was the President of the Moscow Mathematical Society, vice president of the International Congress of Mathematicians, and a full member of the Soviet Academy of Sciences.

Before we go ahead, here is a quick recap on union and intersection.

*Figure 18* is self-explanatory and it shows what is union and intersection which is one of the fundamental concepts of set theory.

Next | Proof of Topology and Topological Space Through Axioms

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:**

- https://mathworld.wolfram.com
- https://www.wikipedia.org/
- https://math.stackexchange.com/
- https://www.researchgate.net/publication/343635292

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,

- Thailand,
- Malaysia,
- Japan,
- The United Kingdom,
- Australia and
- Vietnam

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.