Reserches On The Category Properties Of Lattice Topology And Some Compactnesses

In the first section of this paper, a new kind of paracompactness based on the concept of relative remote neighborhood family in L-topological spaces is established. The relationships between this paracompactness and the other paracompactnesses are discussed. Many properties such as L-good extension, hereditary with respect to closed subsets, weakly topological property and strenthening T2 seperated properties are gotten. And in this section, the sub-base lemma in *-ultra-paracompactness is proved and the subbase lemmas of the other paracompactnesses are also proved by means of the method used in *-ultra-paracompact spaces.In the second section, another application of relative remote neighborhood family is researched. The nearly ultra-fuzzy compactness is generalization of ultra-fuzzy compactness in L-topological spaces. The relationships between this compactness and the other compactness are discussed. It possesses many the properties such as hereditary with respect to regular closed subsets, weakly topoligical property, the subbase lemma and the product theorem. At the same time, the characterizations of the nearly ultra-fuzzy compactness by filters and nets are introduced.In the third section, the concept of SL-closure space is introduced by another LF-set, i.e. semi-closed set. It is a generalization of S-closure operator in L- topological spaces. In this section, its convergence is studied and the SL-continuous generalize order homomorphisms are introduced. The properties and characters of the morphism are gotten. Furthermore, the categorySl-CLOSURE is established and its structure is studied. Some important results, for example Sl-CLOSURE is a topological category over SET w.r.t.Ts where Ts : SL-CLOSURE SET is a forgetful functor, are obtained. At last, the theorem that the functor wSL is the left-adjoint of the functor lSL is proved .