Simon Kwan·Sep 12, 2025Measure Theory — Part 2In part 1, I have introduced the concept of σ-algebra Σ, measure, measurable set, measurable function, simple function and Lebesgue…
Simon Kwan·May 20, 2025Set Theory — Part 1 (Sup and Inf)In this article, I will list out some more advanced concepts in the set theory. I assumed that you have studied the basic set theory…
Simon Kwan·Jan 5, 2025The magic of Artificial Neural Network — Part 4In previous article, I have shown that when Cl(S) is not dense in C(Im) and for every continuous function h∈C(Im)\Cl(S), there exists a…A response icon2A response icon2
Simon Kwan·May 22, 2024The magic of Artificial Neural Network — Part 3This is my third article on the magic of the Artificial Neural Network. I have sketched the proof of the Universal Approximation Theorem…
Simon Kwan·May 14, 2024Hahn-Banach theoremThis is article on the Hahn-Banach theorem. I write this article down to serve both as a note for me as well as a tutorial for the…
Simon Kwan·Apr 10, 2024The magic of Artificial Neural Network — Part 2This is my second article on unlocking the magic of Artificial Neural Network. In part 1, the space of real-valued continuous function…
Simon Kwan·Nov 27, 2023General Topology — Part 7 (Locally Compact Hausdroff Space)In the Locally Compact Hausdroff Space, when a compact set is contained by an open set, a “bump” function over this open set will exist…
