Ultrafilter Modification $M\xi$ (ウルトラフィルター修正) (Section III.1)

• Ultrafilter Modification $M\xi$ (ウルトラフィルター修正) (Section III.1) #Card
  • For a convergence $\xi$ on $X$: $x \in \lim_{M\xi} \mathcal{F}$ whenever $x \in \lim_\xi \mathcal{F}$ and $\mathcal{F}$ is an ultrafilter.

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For a convergence $\xi$ on $X$, define $x \in \lim_{M\xi} \mathcal{F}$ to the effect that $x \in \lim_\xi \mathcal{F}$ and $\mathcal{F}$ is an ultrafilter. Then $M\xi$ is a convergence, called the ultrafilter modification of $\xi$.

参照: cards/topology/prop-iii-1-6（$\xi \neq M\xi$ なら $M\xi$ は有限安定でない）