Dales  within the context of "function algebras" on a compact metrizable space.
First, we note that every (relative) peak set does not necessarily contain a (relative) peak point, even though this is the case for a Banach function algebra on a metrizable space [9, p.
This is equipped with the compact-open topology, and it becomes a compact metrizable space
(possibly infinite dimensional) with the following natural continuous C-action:
Let X be a metrizable space
and let d be a bounded metric on X.
parallel]*[parallel][less than or equal to]n] forms a second countable metrizable space
which leads us to conclude (B(H), [tau]) is again Lindelof.
Since every pseudocompact space is weakly pseudocompact and pseudocompact metrizable space is compact, the following result follows from Theorem 3.
Arhangel'skii, More on remainders close to metrizable spaces, Topology Appl.
Let X be a non compact, locally compact and metrizable space
such that X = [union][K.
Hence (T-spaces, stratifiable spaces, Moore spaces and metrizable spaces
are all D-spaces.
Examples of such spaces are metrizable spaces
and one point compactifications of discrete spaces.