  Based on the theory of ball spaces introduced by Kuhlmann and Kuhlmann we
introduce and study Caristi-Kirk and Oettli-Th\'era ball spaces. We show that
if the underlying metric space is complete, then these have a very strong
property: every ball contains a singleton ball. This fact provides quick proofs
for several results which are equivalent to the Caristi-Kirk Fixed Point
Theorem, namely Ekeland's Variational Principles, the Oettli-Th\'era Theorem,
Takahashi's Theorem and the Flower Petal Theorem.
