Discussion On Some Approximate Compactness In L - Topological Spaces

This paper mainly studied the following contents:In the first chapter, it gives the concept of a strong compactness by a new form of coverage in L-topological spaces. The compactness is strong-Ⅲ Nβ-compactness, which is also strong-Ⅱ Nβ-compactness, strong-Ⅰ Nβ-compactness, Nβ-compactness,S*-compactn-ess and Lowen’s fuzzy compactness. But it is different from PS-compactness. When L=[0,1], strong Nβ-compactness is equivalent to PS-compactness.In the second chapter, By means of strongly semi-open L-sets and their inequality, a new form of SS-closedness is introduced in L-topological spaces, where L is a complete De Morgan algebra. Because L does not require any distributivity, the SS-closedness it has a wider application scope.In the third chapter, we corrected some mathematical errors which are in the Fuzzy Pre-semi-closed Sets(Bul.Malays.Math.Sci.Soc.31(2)(2008),223-232.). Also some new properties of fuzzy pre-semi-closed sets in fuzzy topological spaces are further studied, such as Fps-continuous map, Fps-irresolute map.