>>10993997You do understand that there definition you copy and pasted has nothing to do with the OP text, right? First of all, curvature is defined only on manifolds with an affine connection, hence they possess a differentiable structure (typically a smooth atlas), as well as a Riemannian metric. (I think you can relax to pseudo-Riemannian but that's not relevant). It's not about the topology besides in the implicit existence of a suitable choice of topology which allows these objects (affine connection, metric) to even be defined.
For that matter, I'm pretty sure a disconnected space isn't even T2 in general. How the fuck are you going to talk about curvature on a non-Hausdorff space? (If someone actually knows of a notion of this, I'd be quite interested to hear it.) Not to mention it doesn't even make sense to talk of the "connectedness of curvature". That's a meaningless phrase and is probably why
>>10993625 and
>>10993634 have no idea what you're talking about (as do I).
>does /sci/ only consist of high school faggots with a superiority complex?The irony is fucking palpable here.
