  In this paper, we shall prove some properties of local compactoids and
c-compact sets. At first, we define some concepts similar to the local
compactoidity or the c-compactness, and study relationships between these
concepts and the original ones. As a result, we find a characterization of the
local compactoidity when its coefficient field is spherically complete.
Moreover, from the point of view of the minimum principle, we give a necessary
and sufficient condition for the c-compactness under a suitable condition.
Secondly, we will try a new approach to a non-complete local compactoid, which
gives us a different perspective than before.
