A partially ordered set (E,R) is said to be a tree iff it satisfies the three following conditions:
i) E has a smallest element (called the root );
ii) For every y in E the set of elements x of E such that x R y is finite and linearly ordered by R;
iii) For every element x in E there exists y in E such that x Ry.

If (E,R) is a tree then for every integer n the nth level of (E,R) is the set of elements of E that have exactly n strict predecessors. A subtree of a tree is a subset that is a tree with the induced ordering and is closed under predecessor.

We show that the two following statements are equivalent:
DMC: (Dependent multiple choices) Every tree has a subtree whose levels are finite.
BC: (Baire for Compact spaces) Every compact Hausdorff space is a Baire space.

This solves a question raised by Brunner in [Br83] .

We also prove that the two following statements are equivalent:
DC: The axiom of dependent choices;
BCC: In a Hausdorff locally convex linear topological space, every convex compact convex subset is a Baire space.

It is well known that in ZFA (set theory without the axiom of foundation) the statement DMC does not imply DC, but it is an open question to know if DMC implies DC in set theory ZF.