Quick Revision: Basis and Subbasis (Part 1.2)

Ways to “compress” a topology!

Quick Revision: Topological Spaces (Part 1.1)

The definition of topological spaces and some interesting examples and counterexamples of topological spaces!

Quick Revision: Topology (Part 0)

A series to quickly revise Topology – Dedicated to my students.

Puzzle: Three Connected Sets

Analysis/Topology: Bounded and Totally Bounded Sets

Definitions Bounded set: Let <M,ρ> be a metric space. We say that the subset A of M is bounded if there exists a positive number L such that ρ(x,y)≤L  (x,y∈A) (Wikipedia) Diameter of a set: If A is bounded, we define diameter of A (denoted by diam A) as diam A=  ρ(x,y). If A is not…

Analysis/Topology: Connected Sets in Metric Spaces

A short discussion on Connected Sets in Metric Spaces with definition, examples, counterexamples, properties and quizzes.

Topology/Analysis: Homeomorphism

Definition If is one-one and onto (1-1 correspondence/bijection) continuous is continuous Then we call a homeomorphism between two metric spaces . The metric space  are said to be homeomorphic. Properties and Theorems If f is a homeomorphism between metric spaces , The set G⊂ is open if and only if the image f(G)⊂ is open. The…

Integral Equations and Calculus of Variations: Lecture Notes

Lecture Notes for IECV Coursework at MCC (From archives)

Video Lecture: Examples of Metric Spaces (Lecture 2)

Here’s a video discussing a few simple examples of metric spaces.

Video Lecture: Definition of Metric Spaces (Lecture 1)

Here’s a video discussing the definition of metric spaces, and the inspiration behind it. Rarely