# Category: Pure Mathematics

## 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…

## Puzzle: Finding a Bounded Continuous Function

Find a continuous, real-valued with its range contained in (0, 1).

## Animation: Dihedral Group of Order 8 – Degree 4

Teaching material: Visualization of Dihedral Group of Order 8 – Degree 4. Downloadable.

## CoViD-19: Mathematics Takes a Bullet (John H. Conway)

A collection of links to learn more about John H. Conway, who passed away recently.

## Drawing: Definition of Lebesgue Outer Measure

A cartoon to help learn the definition of Lebesgue Outer Measure.

Also discusses the power of visualization in memorization and Mind Maps, Mind Palace techniques in short.

## 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