# Tagged Questions

**29**

votes

**0**answers

3k views

### Grothendieck's manuscript on topology

Edit: Just in case anyone still thinks that Grothendieck's unpublished manuscripts are (by his letter) entirely out of sight: Declared as "national treasure", they seem to be in principle accessible ...

**17**

votes

**6**answers

3k views

### Why the triangle inequality?

[Maybe this is asking to be closed; but I thought I'd risk it.]
A metric satisfies the axioms:
$d(x,y)=0$ if and only if $x=y$.
$d(x,y) = d(y,x)$.
$d(x,y) \leq d(x,z) + d(z,y)$.
Similarly (and ...

**2**

votes

**1**answer

532 views

### Knowledge base about topology [closed]

We are studying topology. There are a lot of definitions and theorems. I wonder if there somewhere knowledge base about topology and reasoning system exists. So I expect some tool that systematizes ...

**3**

votes

**5**answers

1k views

### Is it true that the only interesting topologies are metric topologies and weak topologies?

In "Infinite dimensional analysis, A hitchhikers guide" by Aliprantis and Border, they write that these 2 classes of topologies "by and large include everything of interest".
@Pete Clarke: I was ...

**19**

votes

**7**answers

2k views

### Why is it useful to classify the vector bundles of a space?

It seems to me that vector bundles are useful because they allow us to bring to bear all of the linear algebra we know to aid in the study of topological spaces. Now, I've read somewhere that it is ...

**25**

votes

**14**answers

2k views

### What are interesting families of subsets of a given set?

Motivation
The usual starting point of both Topology and Measure Theory is the definition of a family of subsets of a set $S$.
Indeed, one defines a topology on $S$ to be a family of subsets ...