In previous articles, I have discussed the definition of a topological space and continuous function. General Topology — Part 1 What is General Topology ?simonkwan-35335.medium.com General Topology — Part 2 ε-δ Definition of Continuous Functionsimonkwan-35335.medium.com In this article, I will discuss some essential topological concepts that are closely related: Neighbourhood, Limit Point, Closed Set, Closure and Dense Set. Let’s start our journey…

ε-δ Definition of Continuous Function Remember the ε-δ definition of Continuous Function that you have learnt in your high school ? A function f : R → R is said to be continuous at x0 ∈ R if ∀ε>0, ∃δ>0 such that|x−x0|<δ ⇒|f(x)−f(x0)|< ε A function is continuous over an open interval if it is…

What is General Topology ? General topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology and algebraic topology. Why should I learn General Topology? Because it is the basic language of modern mathematics…

This is an article for those who are interested in Artificial Neural Network and want to know why it works. In 1989, George Cybenko has published a paper to explain why it works and proved the following theorem, Universal Approximation Theorem: