In the framework of ZF, i.e., Zermelo-Fraenkel set theory without the axiom of choice AC, we show that if the family of all non-empty, closed subsets of a metric space
(
X
,
d
)
(X,d)
has a choice function, then so does the family of all non-empty, open subsets of
X
X
. In addition, we establish that the converse is not provable in ZF. We also show that the statement “every subspace of the real line
R
\mathbb {R}
with the standard topology has a choice function for its family of all closed, non-empty subsets" is equivalent to the weak choice form “every continuum sized family of non-empty subsets of reals has a choice function".