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

摘要

We show that metrizability and bounded tightness are actually equivalent for a large class 9 of locally convex spaces including (LF)-spaces, (DF)-spaces, the space of distributions D'(Omega), etc. A consequence of this fact is that for X is an element of G the bounded tightness for the weak topology of X is equivalent to the following one: X is linearly homeomorphic to a subspace of omega := R-N. This nicely supplements very recent results of Cascales and Raja. Moreover, we show that a metric space X is separable if the space C-p(X) has bounded tightness. (C) 2004 Elsevier Inc. All rights reserved.