Different definitions of locally boundedness of TVS

Question

A susbset $A$ of a topological vector space $E$ is called bounded if for any neighborhood $U$ of the origin there exists a number $\alpha > 0$ such that $\lambda U \supset A$ for any $\lambda \geq \alpha$. The standard definition of locally boundedness for TVS: a topological vector space is locally bounded if it possesses a bounded neighborhood of the origin. On the other hand, in Kolmogorov&Fomin's book, I have encounted with another definition of locally boundedness: a topological vector space is locally bounded if it has at least one non-empty open bounded subset. Are these two definitions equivalent?