A New Class Of Approximate Fuzzy Tight And Closed

As we know, compactness and closeness theory play very important roles in general topology. With the research of the compactness and closeness theory in L-fuzzy topological spaces, many researchers have introduced many kinds of compactness and closeness and further studies showed those compactness and closeness still preserving a lots of good topological properties. In this thesis, we will introduce a new form of SSP-compactness, countably SSP-compactness, SSP-Lindelof property, SSP-closeness and SP-closeness in L-topological spaces by means of SSP-open L-sets, SP-open L-sets and their inequality, and discuss their properties systematically, respectively.In the first part, we give some results which will be used later.In the second part, following the lines of a new definition of fuzzy compact-ness, we introduce a new form of SSP-compactness which is defined by means of strongly semi-preopen L-sets and their inequality in L-topological spaces. It is between Shi's semicompactness and Bai's SP-compactness. This new form of SSP-compactness is described by S-a-R-NF(a-R-NF), S-a-shading(a-shading), S-βa-cover(βa-cover), Qa-cover form and finite intersection property. If L is a complete De Morgan algebra, it has many characterizations.In the third part, we use SSP-compactness as background to introduce the concepts of countably SSP-compactness and SSP-Lindelof property which are characterized by means of SSP-open L-sets and their inequality in L-topological spaces. Their basic properties are studied, and also the R-NF, shading, cover forms and finite intersection properties are described.In the forth part, we introduce a new form of SSP-closeness and SP-closeness in L-topological spaces. The SSP-closeness and SP-closeness are weaker forms of SSP-compactness and SP-compactness and characterized by SSP-open L-sets, SP-open L-sets and their inequality. They are defined for any L-subset, and they are hereditary for SSP-closed subsets and SP-closed subsets, finitely additive, and preserved under SSP-irresolute mapping and SP-irresolute mapping, respectively. Those new notions are good extension and they have many characterizations if L is completely distributive De Morgan algebra.