2020-12-12

## functional analysis – Does the open mapping theorem imply the Baire category theorem?

The Question : 220 people think this question is useful A nice observation by C.E. Blair1, 2, 3 shows that the Baire category theorem for complete metric spaces is equivalent to the axiom of (countable) dependent choice. On the other hand, the three classical consequences of the Baire category theorem in basic functional analysis — the