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Consider the set $[n]=\{1,2,\dots, n\}$. A Kneser $k$-colouring of $[n]$ is a map $c:\mathcal P([n])\to S$ to some set $S$ such that for sets $A_1, A_2,\dots, A_k$ we have $c(A_i)=c(A_j)$ for all $i,j$ implies $\cap_{i=1}^kA_i\ne \varnothing$. Graph theoretically, we want to colour the vertices o...
In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces (for example the Betti numbers) were regarded as derived from combinatorial decompositions of spaces, such as decomposition into simplicial complexes. After the proof of the simplicial approximation theorem this approach provided rigour.
The change of name reflected the move to organise topological classes such as cycles-modulo-boundaries explicitly into abelian groups. This point of view is often attributed to Emmy Noether, and so the change of title may reflect...
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