In this paper semi-developable
spaces are defined and, among T0-spaces, are shown to be the same as the
semimetrizable spaces. Strongly semi-developable spaces are defined in a natural way
and proven to coincide with an important class of semi-mefric spaces, namely those in
which “Cauchy sequences suffice”. These spaces are shown to possess several other
interesting properties. Probably the most significant of these is that the strongly
semi-developable spaces are hereditarily quotient P-images of metric spaces.
Other quotient images of metric spaces are similarly characterized in terms of
semi-developments.
