Manifold fitting, a crucial challenge in nonlinear data analysis, holds immense potential for efficient and accurate modeling. However, existing methods struggle to balance accuracy and computational ...

Metric geometry is a considerable extension of Riemannian geometry that, in recent decades, has proven very useful. A newer direction described in this article can moreover be viewed as an extension ...

In this post I shall discuss the paper “On a Topological Topos” by Peter Johnstone. The basic problem is that algebraic topology needs a “convenient category of spaces” in which to work: the category ...

Then K K is the category of substructures of a countable structure M M which is universal and homogeneous. Examples include the Rado graph as the Fraïssé limit of the category of finite graphs and ...