(Archive) Topological Continuity: Simplicity in Abstraction

Abstraction is often looked down upon by engineers and physicists as something mathematicians do to make life harder for themselves, obfuscate simple things, and make math less applicable in real life. However, the opposite is actually true— restricting your viewpoint to one set or space (say, \( \mathbb{R}^n \)) makes things much more complicated than they have to be. Beauty and simplicity lie in levels of abstraction. Let's take a look at an example, some prerequisites include basic knowledge of metric spaces and topological spaces.