Bounded tightness for locally convex spaces and spaces C(X)

We show that metrizability and bounded tightness are actually equivalent for a large class G of locally convex spaces including (LF)-spaces, (DF)-spaces, the space of distributions D (Ω), etc. A consequence of this fact is that for X ∈ G the bounded tightness for the weak topology of X is equivalent to the following one: X is linearly homeomorphic to a subspace of ω := RN. This nicely supplements very recent results of Cascales and Raja. Moreover, we show that a metric space X is separable if the space Cp(X) has bounded tightness.  2004 Elsevier Inc. All rights reserved