# Tagged Questions

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### Why do we require $X$ to be Hausdorff when defining $C(X)$?

In Efton Park's "Complex Topological K-theory", he begins a section by defining the Banach algebra $C(X)$ (continuous functions $f: X \rightarrow \Bbb C$), presupposing that $X$ is Hausdorff and ...
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### Topological groups, why need them?

I'm reading through Munkres and Armstrong's books on topology. However, I find topological groups to be really complicated objects! I feel they are twice as hard to deal with then just groups and ...
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### What kind of norm is it in the definition of $S^{n-1}$?

Definition (wikipedia) $S^n\triangleq\{x\in\mathbb{R}^{n+1}: ||x||=1\}$ is said to be a 'n-sphere' What norm is it referring to ? I have proven that ...
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### What is the significance of limit points?

When I had my first taste of topology a couple of years ago, our lecturer emphasized the following notions. closed set, closure, closure point open set, interior, interior point Of course, these ...
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### Why the axioms for a topological space are those axioms?

This question might have even been asked here before, I don't really know, so sorry if it's duplicate. I've started to study topological spaces and I've found the axioms for such spaces kind of hard ...
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### motivation of limit points

Lets use Wikipedia's definition of a limit point and let $\lim(A)$ denote the set of limit points of $A$. $a\in \lim (A) \leftrightarrow a\in\operatorname{cl}(A\setminus\{a\})$, \$\lim (A)\cup A = ...
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### Motivation behind topology

What is the motivation behind topology? For instance, in real analysis, we are interested in rigorously studying about limits so that we can use them appropriately. Similarly, in number theory, we ...