# Tagged Questions

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Edit: Just in case anyone still thinks that Grothendieck's unpublished manuscripts are (by his letter) entirely out of sight: Declared as "national treasure", they seem to be in principle accessible ...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