The completeness of the quotient space (topological vector space)
The GoalWe are going to show the completeness of $X/N$ where $X$ is a TVS and $N$ a closed subspace. Alongside, a bunch of us...
Basic Facts of Semicontinuous Functions
ContinuityWe are restricting ourselves into $\mathbb{R}$ endowed with normal topology. Recall that a function is continuous i...
An Introduction to Quotient Space
I’m assuming the reader has some abstract algebra and functional analysis background. You may have learned this already in yo...
More properties of zeros of an entire function
What’s going on againIn this post we discussed the topological properties of the zero points of an entire nonzero function, o...
The Lebesgue-Radon-Nikodym theorem and how von Neumann proved it
An introductionIf one wants to learn the fundamental theorem of Calculus in the sense of Lebesgue integral, properties of mea...
Topological properties of the zeros of a holomorphic function
What’s going onIf for every $z_0 \in \Omega$ where $\Omega$ is a plane open set, the limit \lim_{z \to z_0}\frac{f(z)-f(...