Edit: Just in case anyone still thinks that Grothendieck's unpublished manuscripts are (by his letter) entirely out of sight: Declared as "national treasure", they seem to be in principle accessible ...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