New answers tagged ordinal-numbers
4
votes
Accepted
Restriction of a locally finitely supported function on an ordinal is finitely supported?
If the function has infinitely many nonzero values below some ordinal $\alpha$, let $\beta$ be the supremum of the locations of the first $\omega$ many instances. So $\beta\leq\alpha$ and every ...
- 236k
3
votes
Restriction of a locally finitely supported function on an ordinal is finitely supported?
Yes, this follows from the fact that order topology on any successor ordinal is compact. Let's see a quick proof of this:
Fix a successor ordinal $\alpha+1$ and an open cover $(U_i)_{i \in I}$. Assume ...
- 12.4k
Top 50 recent answers are included