Moore spaces andwΔ-spaces

Metrizability of topological spaces

“…Then, as is easy to check, {^K k : n, k in N} is a G δ -diagonal sequence for X. Since every regular ^-refinable /S-space with a G 5 -diagonal is semi-stratifiable (see [31]), the proof is complete.…”

“…Clearly every countably compact space and every developable space is a wJ-space. In [31] it is proved that every regular wJ-space with a (7-point finite separating open cover is developable.…”

“…See [31], [32], [41]. The idea of characterizing generalized metrizable spaces in the above fashion was first used by Heath in [30].…”

“…(Recall that each Sf Λ is an open collection and that given any two distinct points p and q in X, there is some n such that ord (p, & n ) is finite and there is some G in g^ such that peG, q$G. See [31].) For each pair of positive integers n and k let 3ί?…”

“…Now every regular wJ-space with a σ-point finite separating open cover is developable [31]. Thus Xis a developable ^rcompact space and hence has a countable base [38].…”