# How Surfaces Intersect in Space: An Introduction to Topology

Format: Hardcover
Language: English
Format: PDF / Kindle / ePub
Size: 12.04 MB
Downloadable formats: PDF
Well, according to the Grothendieck school, we should think of a Grothendieck topos as "representing" a space of some kind; but by the very universal property of $\textbf{Sh}(\mathcal{R}^\textrm{op}, \textrm{Zar})$ as a classifying topos, there are as many points of $\textbf{Sh}(\mathcal{R}^\textrm{op}, \textrm{Zar})$ as there are local $R$-algebras – i.e. a proper class! Katzarkov, Branched coverings of CP2 and invariants of symplectic 4-manifolds. Each Non-Euclidean geometry is a consistent system of definitions, assumptions, and proofs that describe such objects as points, lines and planes.
[...]