Tag: baire-category

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

The Question : 212 people think this question is useful I think I remember reading somewhere that the Baire Category Theorem is supposedly quite powerful. Whether that is true or not, it’s my favourite theorem (so far) and I’d love to see some applications that confirm its neatness and/or power. Here’s the theorem (with proof)