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By means of strongly semi-preopen L-sets and their inequality, a new countable SSP-compactness and a new SSP-Lindelöf property are introduced in L-topological spaces, where L is a complete De Morgan algebra. This new form does not depend on the structure of basis lattice L and L does not require any distributivity.
A new concept of near semicompactness is introduced in L-fuzzy topological spaces, where L is a fuzzy lattice. It is weaker than semicompactness and is stronger than S*-closedness. It is described with collection of semiclosed L-fuzzy subsets and finite p-level semiregular-semiopen cover. It is a good L-extension; it is hereditary for semiregular-semiclosed L-fuzzy subsets and semiclopen L-fuzzy subsets;...
The notion of Strong-I Nszlig-compactness is introduced for an arbitrary L-subset and for a complete distributive De Morgan algebra. The strong-I Nszlig-compactness implies Nszlig-compactness, hence it also implies S*-compactness and fuzzy compactness. But it is different from SR-compactness. When L=[0,1], strong-I Nszlig-compactness is equivalent to SR-.compactness.
The convergence theory not only is an significantly basic theory of fuzzy topology and fuzzy analysis but also has wide applications in fuzzy inference and some other aspects. In this paper, we introduce the concept of SSP-closed remote-neighborhood of fuzzy points and establish the Moore-Smith SSP-convergence theory of fuzzy nets. Also we discuss the application of SSP-convergence of fuzzy nets.
In this paper, new characteristic properties of fuzzy Y-continuous mapping are studied, and fuzzy Y-irresolute, fuzzy Y-irresolute open (closed) and fuzzy Y-homoeomorphism mappings are introduced.
The concept of strong pre-connectedness is given on the base of definition of strongly pre-closed sets in L-fuzzy topological spaces. It preserves some fundamental properties of connected sets in general topological spaces. Especially, the famous K. Fan's theorem holds for strong pre-connectivity.
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