A new notion of strong-precompactness in L-topological spaces

In this paper, the concept of strong-precompactness is introduced in L-topological spaces by means of strongly preopen L-sets and their inequality, where L is a complete De Morgan algebra. The new concept does not depend on the structure of basis lattice L which does not require any distributivity. Some fundamental properties of strong-precompactness are obtained. Especially, when L is a completely distributive De Morgan algebra, its many characterizations are presented.