# Is every element from the finite complement topology on R\mathbb R generated by this subbasis a basis element?

A subbasis S\mathbb S for the finite complement topology is the set of all R−x\mathbb R-x where x∈Rx \in \mathbb R. From Munkres I know that the collection of all finite intersections of elements from S\mathbb S forms a basis.

Any finite intersection of elements from S\mathbb S will be a basis element. That is, any set missing finitely many points will be a basis element. But that is every open set in the finite complement topology, besides R\mathbb R.

So, is every element from the finite complement topology generated by this subbasis a basis element?

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