Topology and combinatorics

138 Views Asked by Bumbble Comm At 31 Mar 2026 - 3:15

I'm curious about if there is some interesting research or books about finite topological spaces and combinatorics.

It should answer questions like

How many topologial spaces with $n$ elements and a given property are there?
Do there exist interesting properties exclusive for finite topological spaces? (Just like Lagrange or Sylow theorems in finite groups theory, for example).
Can be those finite topological spaces and/or continuous functions between them classified or represented?

I have found only this.

There are 1 best solutions below

Bumbble Comm On 24 Mar 2018 - 4:01

Try "Algebraic topology of finite topological spaces and its applications":

https://www.google.com.ar/url?sa=t&source=web&rct=j&url=http://www.maths.ed.ac.uk/~v1ranick/papers/barmak2.pdf&ved=2ahUKEwis9dPQqYXaAhVGlpAKHfSgBdYQFjAHegQICRAB&usg=AOvVaw0AfxT5__nz5W6x1o6aUIZX

I think the fist question you mention is still open, though.