Hey guys , i hope you are doing well 😊 .I already told you that i am pursuing my b.sc degree in mathematics and recently i've got the chance to study the topic 'Topology' , which i found very interesting and today i want to share some of the basic concepts of topology with you guys.
Topology which is a basic mathematical discipline and whose name was not coined until 1930s, has now its influence on many branches of pure mathematics especially geometry and analysis and some of the applied too. By pulling a rubber sheet it is obvious by intuition that some of the geometrical properties like length, angle etc. are not preserved while some are retained by such transformation. We call such a change a topological transformation.
We generally define a collection T of subsets of X to be the open sets of X if any union and finite intersection of the elements of T belongs to T and if X and φ ∈T. We call such a collection of sets as a topology on X and (X,T) is said to be a topological space.
To know more about topology, go through the book "Topology by James Munkres". The book has got some good motivations. Give your time and you will love it.
Thanks for reading and take care.