1

I need to prove this statement about matroids: Given $X\in E$, the closure of $X$ is equal to the intersection of all the flats that contain $X$.
Can anybody show me how to solve this? Thank you.

Cornman
  • 11,065
  • 4
  • 30
  • 57
  • What have you tried? – Phicar Jun 20 '21 at 16:07
  • First of all I've proved that the intersection of flats is still a flat. Then if $Y_{1},\dots,Y_{n}$ are the flats, thus: $\bigcap_{i=1}^{n}Y_{i}=X\cup J=cl(X\cup J)$, where $J$ is a set of elements in $Y_{i}\setminus X$, for each $i=1,\dots,n$. Now i should prove that $cl(X\cup J)=cl(X)$, but I don't know how I can do it. –  Jun 20 '21 at 16:27
  • Please read this for further education on how to operate this website. https://math.meta.stackexchange.com/questions/33508/enforcement-of-quality-standards?cb=1 – Cornman Jun 20 '21 at 19:55

0 Answers0