A space is spherically
connected if and only if it has an admissible semi-metric d such that d-spheres of
radius less than one are connected. It is shown that a developable space is
locally connected if and only if it is spherically connected. A semi-metric
space is K-semi-metrizable if and only if it admits a semi-metric d such that
d(A,B) > 0 whenever A and B are disjoint compact sets. It is shown that in
the class of locally connected rim compact spaces, the K-semi-metrizable
spaces are precisely the developable γ-spaces. An example is given of a locally
connected, locally compact K-semi-metrizable Moore space which is not
metrizable.
