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...
关于《第三次忍受》
已经二十五岁，已经不再长个子，家里人决定将我下葬。其实也没什么好抗拒的了，再听一会半通不通的悼词，那些乱七八糟的哭腔和应和，再忍一会棺材里的寒冷，就过去了。这是不是妄想我也不清楚，可我想我大抵是这次死亡的一个配角。 这是不是一场噩梦也无关紧要，尸胺...
The Big Three Pt. 3 - The Open Mapping Theorem (Banach Space)
What is open mappingAn open map is a function between two topological spaces that maps open sets to open sets. Precisely spea...
Cauchy sequence in group theory
Recall - Cauchy sequence in analysisBefore we go into group theory, let’s recall how Cauchy sequence is defined in analysis. ...
A Brief Introduction to Fréchet Derivative
In this post we give a brief introduction too Fréchet derivatives, a generalisation of derivatives in Banach spaces, and deduce *elementary* properties.
An elementary introduction to profinite groups
IntroductionThis blog serves as an introduction to profinite groups without touching anything other than elementary group the...
线性ODE（四）——常系数高阶线性微分方程的普遍解法
最终目标我们要讨论这两种方程的普遍的解决办法 y^{(n)}+a_1y^{(n-1)}+\cdots+a_ny=0\\ y^{(n)}+a_1y^{(n-1)}+\cdots+a_ny=f(x)\\其中$a_i$为常数。在上篇博客里，我们见到了，假...
A continuous function is 'mostly' nowhere differentiable
About this postIt is taught in elementary calculus course that, if a function is differentiable at some point $x_0$, then it’...
The Big Three Pt. 2 - The Banach-Steinhaus Theorem
About this blog postPeople call the Banach-Steinhaus theorem the first of the big three, which sits at the foundation of line...
The Big Three Pt. 1 - Baire Category Theorem Explained
About the ‘Big Three’There are three theorems about Banach spaces that occur frequently in the crux of functional analysis, w...